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action

(ăk'shən)

The state or process of acting or doing: The medical team went into action.
Something done or accomplished; a deed. See Usage Note at act.
Organized activity to accomplish an objective: a problem requiring drastic action.
The causation of change by the exertion of power or a natural process: the action of waves on a beach; the action of a drug on blood pressure.
A movement or a series of movements, as of an actor.
Manner of movement: a horse with fine action.
Habitual or vigorous activity; energy: a woman of action.
Behavior or conduct. Often used in the plural.
1. The operating parts of a mechanism.
2. The manner in which such parts operate.
3. The manner in which a musical instrument can be played; playability: a piano with quick action.
The series of events and episodes that form the plot of a story or play.
The appearance of animation of a figure in painting or sculpture.
Law. A judicial proceeding whose purpose is to obtain relief at the hands of a court.
1. Armed encounter; combat: missing in action.
2. An engagement between troops or ships: fought a rear-guard action.
The most important or exciting work or activity in a specific field or area: always heads for where the action is.

actionless ac'tion·less adj.

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Library

Sci-Tech Encyclopedia: Action

Any one of a number of related integral quantities which serve as the basis for general formulations of the dynamics of both classical and quantum-mechanical systems. The term has been associated with four quantities: the fundamental action S, for general paths of a dynamical system; the classical action S_C, for the actual path; the modified action S′, for paths restricted to a particular energy; and action variables, for periodic motions.

A dynamical system can be described in terms of some number N of coordinate degrees of freedom that specify its configuration. As the vector q whose components are the degrees of freedom q₁, q₂, …, q_N varies with time t, it traces a path q(t) in an N-dimensional space. The fundamental action S is the integral of the lagrangian of the system taken along any path q(t), actual or virtual, starting from a specified configuration q₁ at a specified time t₁, and ending similarly at configuration q₂ and time t₂. The value of this action S[q(t)] depends on the particular path q(t). The actual path q_C(t) which is traversed when the system moves according to newtonian classical mechanics gives an extremum value of S, usually a minimum, relative to the other paths. This is Hamilton's least-action principle. The extremum value depends only on the end points and is called the classical action S_C(q₁, q₂; t₁, t₂).

An important variant of Hamilton's principle applies when the virtual paths q(t) are restricted to motions all of the same energy E, but no longer to a specific time interval, t₁ − t₂. The modified action S′ = S − E(t₁ − t₂) obeys a modified least-action principle, usually called Maupertuis' principle, namely, that the classical path gives again an extremal value of S′ relative to all paths of that energy. Maupertuis' principle is closely related to Fermat's principle of least time in classical optics for the path of light rays of a definite frequency through a region of inhomogeneous refractive index. See also Hamilton's principle; Minimal principles.

In quantum mechanics, as originally formulated by E. Schrödinger, the state of particles is described by wave functions which obey the Schrödinger wave equation. States of definite energy in, say, atoms are described by stationary wave functions, which do not move in space. Nonstationary wave functions describe transitory processes such as the scattering of particles, in which the state changes. Both stationary and nonstationary state wave functions are determined, in principle, once the Schrödinger wave propagator (also called the Green function) between any two points q₁ and q₂ is known. In a fundamental restatement of quantum mechanics, R. Feynman showed that all paths from q₁ to q₂, including the virtual paths, contribute to the wave propagator. Each path contributes a complex phase-term exp i (φ[q(t)]), where the phase φ is proportional to the action for that path. The resulting sum over paths, appropriately defined, is the path integral (or functional integral) representation of the Schrödinger wave propagator. The path integral has become the general starting point for most formulations of quantum theories of particles and fields. The classical path q_C(t) of least action now plays the role in the wave function as being the path of stationary phase. See also Propagator (field theory).

Marketing Dictionary: action

Advertising: impelling function of advertising. Almost all advertising is based on some action that the advertiser wants individuals to take. The desired action may be to move people directly to the purchase of a product (direct action), or it can be more subtle-for example, to move individuals toward a new thinking pattern in which the product or service is seen in a favorable light. An example of action-oriented advertising is the political advertisement, where the immediate desired objective is to generate positive feelings about the candidate and where the longer range desired action is to move the public to vote for the candidate. Two other examples are the price-off coupon offer in a print advertisement, where the desired action is the clipping of a coupon by the consumer and his or her subsequent purchase of the product, and the retail store sale advertisement designed to motivate the consumer to come to the store and shop.

Film or television production:

1.any motion by performers on the viewing screen that is intended to be transmitted or recorded.

2.order to begin movement in filming, as in "Lights, camera, action."

Thesaurus: action

noun

The process of doing: act. See action/inaction.
Something done: act, deed, doing, thing, work. See do/not do.
The manner in which one behaves. behavior, comportment, conduct, deportment, way. See be.
A legal proceeding to demand justice or enforce a right: case, cause, instance, lawsuit, suit. See law.
A hostile encounter between opposing military forces: battle, combat, engagement. See conflict/cooperation.

Idioms: action

In addition to the idioms beginning with action, also see all talk and no action; piece of the action; swing into action.

Antonyms: action

Definition: something done
Antonyms: cessation, idleness, inaction, inactivity, inertia, repose, rest, stoppage

US Military Dictionary: action

n. 1. armed conflict.

2. a military engagement: a rearguard action.

3. a manner or style of doing something, typically the way in which a mechanism works or a person moves.

go into action start battle.

in action engaged in battle.

See the Introduction, Abbreviations and Pronunciation for further details.

Philosophy Dictionary: action

What an agent does, as opposed to what happens to an agent (or even what happens inside an agent's head). Describing events that happen does not of itself permit us to talk of rationality and intention, which are the categories we may apply if we conceive of them as actions. We think of ourselves not only passively, as creatures within which things happen, but actively, as creatures that make things happen. Understanding this distinction gives rise to major problems concerning the nature of agency, of the causation of bodily events by mental events, and of understanding the will and free will. Other problems in the theory of action include drawing the distinction between an action and its consequences, and describing the structures involved when we do one thing ‘by’ doing another thing. Even the placing and dating of action can give rise to puzzles, as in cases where someone shoots someone on one day and in one place, and the victim then dies on another day and in another place. Where and when did the murder take place?

Sports Science and Medicine: action

1. Any unit or sequence of social activity or behaviour. The term is sometimes restricted to social activities, which are intentional and involve conscious deliberation, rather than merely being the result of a behavioural reflex.

2. In biomechanics, the product of work and time. Compare power.

3. See muscle action.

US History Encyclopedia: ACTION

Action was a federal agency established by President Richard Nixon on 1 July 1971. Its intention was to make the service organizations established during the 1960s operate more efficiently. The programs absorbed were the Active Corps of Executives, the Peace Corps, the Retired Senior Volunteer Program, the Service Corps of Retired Executives, the National Student Volunteer Program, and Volunteers in Service to America (VISTA). In the 1980s, the Reagan administration urged private groups to take some of the load borne by VISTA, and VISTA itself was cut in personnel, thereby diminishing the power and influence of ACTION. In 1990, the National and Community Service Act further weakened ACTION's administrative role, and in 1993, the National and Community Service Trust Act absorbed ACTION into the Corporation for National and Community Service.

Bibliography

"The National and Community Service Act of 1990." Available from http://www.cns.gov/about/ogc/legislation.html.

United States Congress, Senate Committee on Labor and Public Welfare, Special Subcommittee on Human Resources. Action Act of 1972 and Action Domestic Programs. Joint hearing before the Special Subcommittee on Human Resources and the Subcommittee on Aging of the Committee on Labor and Public Welfare, United States Senate, 92nd Congress, Second session on S. 3450…and related bills, Older Americans Action Programs. Washinton, D.C.: Government Printing Office, 1972.

—Kirk H. Beetz

Law Encyclopedia: Action

This entry contains information applicable to United States law only.

Conduct; behavior; something done; a series of acts.

A case or lawsuit; a legal and formal demand for enforcement of one's rights against another party asserted in a court of justice.

The term action includes all the proceedings attendant upon a legal demand, its adjudication, and its denial or its enforcement by a court. Specifically, it is the legal proceedings, while a cause of action is the underlying right that gives rise to them. In casual conversation, action and cause of action may be used interchangeably, but they are more properly distinguished. At one time, it was more correct to speak of actions at law and of proceedings or suits in equity. The distinction is rather technical, however, and not significant since the merger of law and equity. The term action is used more often for civil lawsuits than for criminal proceedings.

Parties in an Action

A person must have some sort of legal right before starting an action. That legal right implies a duty owed to one person by another, whether it is a duty to do something or a duty not to do something. When the other person acts wrongfully or fails to act as the law requires, such behavior is a breach, or violation, of that person's legal duty. If that breach causes harm, it is the basis for a cause of action. The injured person may seek redress by starting an action in court.

The person who starts the action is the plaintiff, and the person sued is the defendant. They are the parties in the action. Frequently, there are multiple parties on a side. The defendant may assert a defense which, if true, will defeat the plaintiff's claim. A counterclaim may be made by the defendant against the plaintiff or a cross-claim against another party on the same side of the lawsuit. The law may permit joinder of two or more claims, such as an action for property damage and an action for personal injuries, after one auto accident; or it may require consolidation of actions by an order of the court. Where prejudice or injustice is likely to result, the court may order a severance of actions into different lawsuits for different parties.

Commencement of an Action

The time when an action may begin depends on the kind of action involved. A plaintiff cannot start a lawsuit until the cause of action has accrued. For example, a man who wants to use a parcel of land for a store where only houses are allowed must begin by applying for a variance from the local zoning board. He cannot bypass the board and start an action in court. His right to sue does not accrue until the board turns down his request.

Neither can a person begin an action after the time allowed by law. Most causes of action are covered by a statute of limitations, which specifically limits the time within which to begin the action. If the law in a particular state says that an action for libel cannot be brought more than one year after publication of a defamatory statement, then those actions must be initiated within that statutory period. Where there is no statute that limits the time to commence a particular action, a court may nevertheless dismiss the case if the claim is stale and if litigation at that point would not be fair.

A plaintiff must first select the right court, then an action can be commenced by delivery of the formal legal papers to the appropriate person. Statutes that regulate proper procedure for this must be strictly observed. A typical statute specifies that an action may be begun by delivery of a summons, or a writ on the defendant. At one time, common-law actions had to be pleaded according to highly technical forms of action, but now it is generally sufficient simply to serve papers that state facts describing a recognized cause of action. If this service of process is done properly, the defendant has fair notice of the claim made against him or her and the court acquires jurisdiction over him or her. In some cases, the law requires delivery of the summons or writ to a specified public officer such as a U.S. marshal, who becomes responsible for serving it on the defendant.

Termination of an Action

After an action is commenced, it is said to be pending until termination. While the action is pending, neither party has the right to start another action in a different court over the same dispute or to do any act that would make the court's decision futile.

A lawsuit may be terminated because of dismissal before both sides have fully argued the merits of their cases at trial. It can also be ended because of compromise and settlement, after which the plaintiff withdraws his or her action from the court.

Actions are terminated by the entry of final judgments by the courts. A judgment may be based on a jury verdict or it may be a judgment notwithstanding the verdict. Where there has been no jury, judgment is based on the judge's decision. Unless one party is given leave — or permission from the court — to do something that might revive the lawsuit, such as amending an insufficient complaint, the action is at an end when judgment is formally entered on the records of the court.

See: civil procedure.

Veterinary Dictionary: action

1. the accomplishment of an effect, whether mechanical or chemical, or the effect so produced.
2. the gait or type of movement of an animal.

cumulative a. — the sudden and markedly increased action of a drug after administration of several doses.
a. lists — are produced by a computerized herd health program from the analysis of reproduction data, which set out which cows are to be examined for a variety of reproductive reasons, such as pregnancy, failure to conceive and postnatal clearance for resumption of breeding.

Word Tutor: action

IN BRIEF: The process of doing something.

No action is without its side effects. — Barry Commoner, US biologist, environmentalist, major advocate of environmental protection.

Tutor's tip: Most art collectors take "action" (act) when attending an "auction" (sale at which people bid against one another for an item).

Quotes About: Action

Quotes:

"In this country men seem to live for action as long as they can and sink into apathy when they retire." - Charles Francis Adams

"You can tell more about a person by what he says about others than you can by what others say about him." - Leo Aikman

"The shortest distance between two points is under construction." - Noelie Alito

"The greatest potential for control tends to exist at the point where action takes place." - Loius A. Allen

"Action is coarsened thought; thought becomes concrete, obscure, and unconscious." - Henri Frederic Amiel

"Action and faith enslave thought, both of them in order not be troubled or inconvenienced by reflection, criticism, and doubt." - Henri Frederic Amiel

See more famous quotes about Action

Wikipedia: action (physics)

In physics, the action is a particular quantity in a physical system that can be used to describe its operation in an alternative manner to the usual differential equation approach. The action is not necessarily the same for different types of system.

The contemporary action approach for physical systems yields the same results as those found using differential equations to describe the system, but only requires the states of the physical variable to be specified at two points, called the initial and final states. The values of the physical variable at all intermediate points may then be determined by 'minimizing' the action.

History of term 'action'

The term "action" was defined in several (now obsolete) ways during its development.

Gottfried Leibniz, Johann Bernoulli and Pierre Louis Maupertuis defined the "action" for light as the integral of its speed (or inverse speed) along its path length.
Leonhard Euler (and, possibly, Leibniz) defined it for a material particle as the integral of the particle speed along its path through space.
Maupertuis introduced several ad hoc and contradictory definitions of "action" within a single article, defining action as potential energy, as virtual kinetic energy, and as a strange hybrid that ensured conservation of momentum in collisions.

Concepts

Physical laws are most often expressed as differential equations, which specify how a physical variable changes from its present value with infinitesimally small changes in time or position or some other variable. By adding up these small changes, a differential equation provides a recipe for determining the value of the physical variable at any point, given only its starting value at one point and possibly some initial derivatives.

The action takes a different but equivalent approach that yields the same results as the differential equation but only requires the states of the physical variable to be specified at two points, called the initial and final states. The values of the physical variable at all intermediate points may then be determined by 'minimizing' the action.

The equivalence of these two approaches is contained in Hamilton's principle which states that the differential equations of motion for any physical system can be re-formulated as an equivalent integral equation. It applies not only to the classical mechanics of a single particle, but also to classical fields such as the electromagnetic and gravitational fields.

Hamilton's principle has also been extended to quantum mechanics and quantum field theory.

Mathematical definition

Expressed in mathematical language,using the calculus of variations, the evolution of a physical system (i.e. how the system actually progresses from one state to another) corresponds to an extremum (usually, a minimum) of the action.

Several different definitions of 'the action' are in common use in physics:

The action is usually an integral over time. But for action pertaining to fields, it may be integrated over spatial variables as well. In some cases, the action is integrated along the path followed by the physical system.

The evolution of a physical system between two states is determined by requiring the action be minimized or, more generally, be stationary for small perturbations about the true evolution. This requirement leads to differential equations that describe the true evolution.

Conversely, an action principle is a method for reformulating differential equations of motion for a physical system as an equivalent integral equation. Although several variants have been defined (see below), the most commonly used action principle is Hamilton's principle.

An earlier, less informative action principle is Maupertuis' principle, which is sometimes called by its (less correct) historical name, the principle of least action.

Disambiguation of "action" in classical physics

In classical physics, the term action has at least eight distinct meanings.

Action (functional)

Most commonly, the term is used for a functional $\mathcal{S}$ which takes a function of time and (for fields) space as input and returns a scalar. Specifically, in classical mechanics, the input function is the evolution $\mathbf{q}(t)$ of the system between two time points $t 1$ and $t 2$ , where $\mathbf{q}$ represent the generalized coordinates. The action $\mathcal{S}[\mathbf{q}(t)]$ is defined as the integral of the Lagrangian $L$ for an input evolution between the two time points

$\mathcal{S}[\mathbf{q}(t)] = \int_{t_1}^{t_2} L[\mathbf{q}(t),\dot{\mathbf{q}}(t),t]\, \mathrm{d}t$

where the endpoints of the evolution are fixed and defined as $\mathbf{q}_{1} = \mathbf{q}(t_{1})$ and $\mathbf{q}_{2} = \mathbf{q}(t_{2})$ . According to Hamilton's principle, the true evolution $\mathbf{q}_{\mathrm{true}}(t)$ is an evolution for which the action $\mathcal{S}[\mathbf{q}(t)]$ is stationary (a minimum, maximum, or a saddle point). This principle results in the equations of motion in Lagrangian mechanics.

Abbreviated action (functional)

Usually denoted as $\mathcal{S}_{0}$ , this is also a functional. Here the input function is the path followed by the physical system without regard to its parameterization by time. For example, the path of a planetary orbit is an ellipse, and the path of a particle in a uniform gravitational field is a parabola; in both cases, the path does not depend on how fast the particle traverses the path. The abbreviated action $\mathcal{S}_{0}$ is defined as the integral of the generalized momenta along a path in the generalized coordinates

$\mathcal{S}_{0} = \int \mathbf{p} \cdot \mathrm{d}\mathbf{q}$

According to Maupertuis' principle, the true path is a path for which the abbreviated action $\mathcal{S}_{0}$ is stationary.

Hamilton's principal function

Hamilton's principal function is defined by the Hamilton–Jacobi equations (HJE), another alternative formulation of classical mechanics. This function $S$ is related to the functional $\mathcal{S}$ by fixing the initial time $t 1$ and endpoint $\mathbf{q}_{1}$ and allowing the upper limits $t 2$ and the second endpoint $\mathbf{q}_{2}$ to vary; these variables are the arguments of the function $S$ . In other words, the action function $S$ is the indefinite integral of the Lagrangian with respect to time.

Hamilton's characteristic function

When total energy $E$ is conserved, the HJE can be solved with the time-independent function $W(q_{1},\dots,q_{N}) = S(q_{1},\dots,q_{N},t) - E\cdot t$ , which is called Hamilton's characteristic function. (See Hamilton–Jacobi equations: Separation of variables.)

Action of a generalized coordinate

This is a single variable $J k$ in the action-angle coordinates, defined by integrating a single generalized momentum around a closed path in phase space, corresponding to rotating or oscillating motion

$J_{k} = \oint p_{k} \mathrm{d}q_{k}$

The variable $J k$ is called the "action" of the generalized coordinate $q k$ ; the corresponding canonical variable conjugate to $J k$ is its "angle" $w k$ , for reasons described more fully under action-angle coordinates. The integration is only over a single variable $q k$ and, therefore, unlike the integrated dot product in the abbreviated action integral above. The $J k$ variable equals the change in $S k (q k)$ as $q k$ is varied around the closed path. For several physical systems of interest, $J k$ is either a constant or varies very slowly; hence, the variable $J k$ is often used in perturbation calculations and in determining adiabatic invariants.

Action for a Hamiltonian flow

See tautological one-form.

Euler-Lagrange equations for the action integral

As noted above, the requirement that the action integral be stationary under small perturbations of the evolution is equivalent to a set of differential equations (called the Euler-Lagrange equations) that may be determined using the calculus of variations. We illustrate this derivation here using only one coordinate, x; the extension to multiple coordinates is straightforward.

Adopting Hamilton's principle, we assume that the Lagrangian L (the integrand of the action integral) depends only on the coordinate x(t) and its time derivative dx(t)/dt, and does not depend on time explicitly. In that case, the action integral can be written

$\mathcal{S} = \int_{t_1}^{t_2}\; L(x,\dot{x})\,\mathrm{d}t$

where the initial and final times ( $t 1$ and $t 2$ ) and the final and initial positions are specified in advance as $x 1 = x (t 1)$ and $x 2 = x (t 2)$ . Let $x true (t)$ represent the true evolution that we seek, and let $x per (t)$ be a slightly perturbed version of it, albeit with the same endpoints, $x per (t 1) = x 1$ and $x per (t 2) = x 2$ . The difference between these two evolutions, which we will call $\varepsilon(t)$ , is infinitesimally small at all times

$\varepsilon(t) = x_{\mathrm{per}}(t) - x_{\mathrm{true}}(t)$

At the endpoints, the difference vanishes, i.e., $\varepsilon(t_{1}) = \varepsilon(t_{2}) = 0$ .

Expanded to first order, the difference between the actions integrals for the two evolutions is

Failed to parse (unknown function\begin): \begin{align} \delta \mathcal{S} &= \int_{t_1}^{t_2}\; \left[ L(x_{\mathrm{true}}+\varepsilon,\dot x_{\mathrm{true}} +\dot\varepsilon)- L(x_{\mathrm{true}},\dot x_{\mathrm{true}}) \right]dt \\ &= \int_{t_1}^{t_2}\; \left(\varepsilon{\partial L\over\partial x} + \dot\varepsilon{\partial L\over\partial \dot x} \right)\,\mathrm{d}t \end{align}

Integration by parts of the last term, together with the boundary conditions $\varepsilon(t_{1}) = \varepsilon(t_{2}) = 0$ , yields the equation

$\delta \mathcal{S} = \int_{t_1}^{t_2}\; \left( \varepsilon{\partial L\over \partial x} - \varepsilon{d\over dt }{\partial L\over\partial \dot x} \right)\,\mathrm{d}t.$

The requirement that $\mathcal{S}$ be stationary implies that the first-order change $\delta\mathcal{S}$ must be zero for any possible perturbation $\varepsilon(t)$ about the true evolution. This can be true only if

${\partial L\over\partial x} - {\mathrm{d}\over \mathrm{d}t }{\partial L\over\partial \dot{x}} = 0$ Euler-Lagrange equation

Those familiar with functional analysis will note that the Euler-Lagrange equations simplify to

$\frac{\delta \mathcal{S}}{\delta x(t)}=0$ .

The quantity $\frac{\partial L}{\partial\dot x}$ is called the conjugate momentum for the coordinate x. An important consequence of the Euler-Lagrange eqations is that if L does not explicitly contain coordinate x, i.e.

if $\frac{\partial L}{\partial x}=0$ , then $\frac{\partial L}{\partial\dot x}$ is constant.

In such cases, the coordinate x is called a cyclic coordinate, and its conjugate momentum is conserved.

Example: Free particle in polar coordinates

Simple examples help to appreciate the use of the action principle via the Euler-Lagrangian equations. A free particle (mass m and velocity v) in Euclidean space moves in a straight line. Using the Euler-Lagrange equations, this can be shown in polar coordinates as follows. In the absence of a potential, the Lagrangian is simply equal to the kinetic energy

$\frac{1}{2} mv^2= \frac{1}{2}m \left( \dot{x}^2 + \dot{y}^2 \right)$

in orthonormal (x,y) coordinates, where the dot represents differentiation with respect to the curve parameter (usually the time, t). In polar coordinates (r, φ) the kinetic energy and hence the Lagrangian becomes

$L = \frac{1}{2}m \left( \dot{r}^2 + r^2\dot\varphi^2 \right).$

The radial r and φ components of the Euler-Lagrangian equations become, respectively

Failed to parse (unknown function\begin): \begin{align} \frac{\mathrm{d}}{\mathrm{d}t} \left( \frac{\partial L}{\partial \dot{r}} \right) - \frac{\partial L}{\partial r} &= 0 \qquad \Rightarrow \qquad \ddot{r} - r\dot{\varphi}^2 &= 0 \\ \frac{\mathrm{d}}{\mathrm{d}t} \left( \frac{\partial L}{\partial \dot{\varphi}} \right) - \frac{\partial L}{\partial \varphi} &= 0 \qquad \Rightarrow \qquad \ddot{\varphi} + \frac{2}{r}\dot{r}\dot{\varphi} &= 0 \end{align}

The solution of these two equations is given by

Failed to parse (unknown function\begin): \begin{align} r\cos\varphi &= a t + b \\ r\sin\varphi &= c t + d \end{align}

for a set of constants a, b, c, d determined by initial conditions. Thus, indeed, the solution is a straight line given in polar coordinates.

Action principle for classical fields

The action principle can be extended to obtain the equations of motion for fields, such as the electromagnetic field or gravity.

The Einstein equation utilizes the Einstein-Hilbert action as constrained by a variational principle.

The path of a body in a gravitational field (i.e. free fall in space time, a so called geodesic) can be found using the action principle.

Action principle in quantum mechanics and quantum field theory

In quantum mechanics, the system does not follow a single path whose action is stationary, but the behavior of the system depends on all imaginable paths and the value of their action. The action corresponding to the various paths is used to calculate the path integral, that gives the probability amplitudes of the various outcomes.

Although equivalent in classical mechanics with Newton's laws, the action principle is better suited for generalizations and plays an important role in modern physics. Indeed, this principle is one of the great generalizations in physical science. In particular, it is fully appreciated and best understood within quantum mechanics. Richard Feynman's path integral formulation of quantum mechanics is based on a stationary-action principle, using path integrals. Maxwell's equations can be derived as conditions of stationary action.

Action principle and conservation laws

Symmetries in a physical situation can better be treated with the action principle, together with the Euler-Lagrange equations, which are derived from the action principle. An example is Noether's theorem, which states that to every continuous symmetry in a physical situation there corresponds a conservation law (and conversely). This deep connection requires that the action principle be assumed.

Modern extensions of the action principle

The action principle can be generalized still further. For example, the action need not be an integral because nonlocal actions are possible. The configuration space need not even be a functional space given certain features such as noncommutative geometry. However, a physical basis for these mathematical extensions remains to be established experimentally.

References

For an annotated bibliography, see Edwin F. Taylor [1] who lists, among other things, the following books

Cornelius Lanczos, The Variational Principles of Mechanics (Dover Publications, New York, 1986). ISBN 0-486-65067-7. The reference most quoted by all those who explore this field.
L. D. Landau and E. M. Lifshitz, Mechanics, Course of Theoretical Physics (Butterworth-Heinenann, 1976), 3rd ed., Vol. 1. ISBN 0-7506-2896-0. Begins with the principle of least action.
Thomas A. Moore "Least-Action Principle" in Macmillan Encyclopedia of Physics (Simon & Schuster Macmillan, 1996), Volume 2, ISBN 0-02-897359-3, OCLC 35269891, pages 840 – 842.
David Morin introduces Lagrange's equations in Chapter 5 of his honors introductory physics text. Concludes with a wonderful set of 27 problems with solutions. A draft of is available at [2]
Gerald Jay Sussman and Jack Wisdom, Structure and Interpretation of Classical Mechanics (MIT Press, 2001). Begins with the principle of least action, uses modern mathematical notation, and checks the clarity and consistency of procedures by programming them in computer language.
Dare A. Wells, Lagrangian Dynamics, Schaum's Outline Series (McGraw-Hill, 1967) ISBN 0-07-069258-0, A 350 page comprehensive "outline" of the subject.
Robert Weinstock, Calculus of Variations, with Applications to Physics and Engineering (Dover Publications, 1974). ISBN 0-486-63069-2. An oldie but goodie, with the formalism carefully defined before use in physics and engineering.
Wolfgang Yourgrau and Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory (Dover Publications, 1979). A nice treatment that does not avoid the philosophical implications of the theory and lauds the Feynman treatment of quantum mechanics that reduces to the principle of least action in the limit of large mass.
Edwin F. Taylor's page [3]
Principle of least action interactive Excellent interactive explanation/webpage

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Translations: Translations for: Action

Dansk (Danish)
n. - aktion, handling, iværksættelse
v. tr. - handle, iværksætte

idioms:

action group aktionsudvalg, aktionskommite
action point handlingsplan, afgørelse
action replay genafspilning, langsom gengivelse
action stations kampberedskab, kampklar position
bring into action tage i brug
go into action gå i aktion, skride til handling
out of action ude af drift
put into action gøre funktionsdygtig, gøre kampklar
take action skride til handling, gå i aktion, handle

Nederlands (Dutch)
actie, handeling/daad, werking, gevechtshandeling, manier van bewegen/ functioneren, rechtszaak, een rechtszaak aanspannen tegen

Français (French)
n. - action, effet, usage, service, combat, acte, (Théât) intrigue, (Cin) moteur, (Jur) procès, action en justice, (Tech) mécanisme, marche, (Mil) combat, engagement
v. tr. - (Admin) exécuter

idioms:

action group groupe d'action
action point séquence, point actif
action replay (GB, TV, Sport) répétition immédiate d'une séquence, ralenti
action stations (Mil) postes de combats
bring into action engager, atteler, porter à l'action
go into action aller ou marcher au combat
in action (tué) au combat
out of action hors d'usage
put into action mettre à exécution, mettre en action ou en pratique, mettre en marche
take action agir, prendre des mesures

Deutsch (German)
n. - Handlung, Tat, Arbeit, Funktion, Wirkung , Einfluss, Gefecht, Kampf, Kampfhandlung, (Tech.) Mechanik, (Tech.) Auslöser, (Rechtsw.) Klage, (Rechtsw.) Prozess
v. - etw. unternehmen, einen Prozess gegen jmdn. anstrengen, jmdn.verklagen

idioms:

action group Aktionsgemeinschaft, Bürgerinitiative, Interessengemeinschaft
action point Handlungsvorschlag
action replay (Zeitlupen)wiederholung
action stations Gefechtsstationen
bring into action einsetzen, aufbieten
go into action in Aktion treten, eingreifen
in action in Betrieb, im Kampf
out of action außer Gefecht
put into action einsetzen, aufbieten
take action handeln, tätig werden, verfahren, vorgehen

Ελληνική (Greek)
n. - δράση, ενέργεια, πράξη, επενέργεια, επίδραση, μάχη, πολεμική δραστηριότητα, (νομ.) αγωγή, μήνυση, λειτουργία, έντονη δραστηριότητα, κινητοποίηση, (μτφ.) ψυχαγωγία, διασκέδαση, (καθομ.) τζόγος

idioms:

action group ομάδα δράσης
action point απόφαση προς εκτέλεση
action replay επανάληψη φάσης
action stations (στρατ.) θέσεις μάχης
bring into action ενεργοποιώ, θέτω σε ενέργεια
go into action αναλαμβάνω δράση
out of action εκτός λειτουργίας, (μτφ.) εκτός μάχης
put into action θέτω σε ενέργεια ή εφαρμογή
take action ενεργώ, δρω, αναλαμβάνω δράση, δραστηριοποιούμαι

Italiano (Italian)
azione, scontro, operazione, attività, manovra, scenario

idioms:

a slice of the action partecipazione
action group comitato d'azione
action point progetto d'azione
action replay ripresa
action stations posti di combattimento
bring into action mettere in azione, mettere in moto
freedom of action libertà d'azione
go into action entrare in azione, passare all'azione
legal action causa
lightning action azione fulminea
line of action direttiva
out of action inattivo, fuori allenamento
put into action mettere in moto, mettere in azione
radius of action raggio d'azione
sphere of action sfera d'azione
take action procedere

Português (Portuguese)
n. - ação (f), atividade (f), ato (m), acionamento (m), mecanismo (m), batalha (f), iniciativa (f)

idioms:

a piece of the action divisão (f) de trabalho, divisão (f) de lucros, oportunidade (f) de ganhos financeiros
a slice of the action fatia (f) dos ganhos (Fin.)
action group grupo (m) de atividade
action point ponto (m) de ação
action replay repetição (f) de ação
action stations estações (f pl) de ação
affirmative action ação afirmativa (Jur.)
bring into action colocar em ação
freedom of action liberdade (f) de ação
go into action entrar em ação
legal action ação legal (Jur.)
lightning action ação relâmpago
line of action linha (f) de ação
out of action inutilizado
put into action colocar em ação
radius of action raio (m) de ação
sphere of action esfera (f) de ação
take action agir, iniciar o trabalho, processar

Русский (Russian)
действие, меры (против кого-то, чего-то), бой, действие, работа, деятельность, маневр, сюжет

idioms:

a piece of the action доход с какого-либо мероприятия
a slice of the action доход с какого-либо мероприятия
action group группа, созданная для принятия мер
action point предложение действия после обсуждения
action replay проигрывание назад кадров спортивный матчей
action replay проигрывание вновь кадров фильма
action stations боевые посты
affirmative action утверждение, подтверждение; действие (в отличие от бездействия)
bring into action задействовать, привести в действие
freedom of action свобода действий
go into action вступать в бой
legal action судебные действия, судебное преследование
lightning action молниеносные действия
line of action линия поведения
out of action не способный более работать, действовать
put into action задействовать что-либо
radius of action радиус действия
sphere of action сфера влияния
take action принимать меры

Español (Spanish)
n. - acción, actuación, lucha, batalla, combate, acto, actividad, animación, movimiento, maniobra, trama, argumento, intriga
v. tr. - accionar, actuar, luchar, batallar, combatir, animar, mover, maniobrar

idioms:

action group comité de acción
action point punto de acción
action replay repetición de la jugada
action stations puestos de combate
bring into action poner en movimiento
go into action entrar en acción
in action en acción , funcionando, operando
out of action inutilizar, estropear
put into action poner en práctica
take action tomar medidas, intentar una acción judicial

Svenska (Swedish)
n. - handling, inverkan, funktion

中文（简体） (Chinese (Simplified))
动作, 战斗, 作用, 对...起诉

idioms:

action group 行动小组
action point 行动时刻
action replay 实时回放, 可实时回放的镜头, 立刻重演
action stations 战斗位置, 各就各位
bring into action 使开始行动
go into action 投入战斗
out of action 出故障, 不活动, 不运转
put into action 进入行动, 把...付诸实施
take action 采取行动, 提出诉讼

中文（繁體） (Chinese (Traditional))
n. - 動作, 戰鬥, 作用
v. tr. - 對...起訴

idioms:

action group 行動小組
action point 行動時刻
action replay 即時重播, 可即時重播的鏡頭, 立刻重演
action stations 戰鬥位置, 各就各位
bring into action 使開始行動
go into action 投入戰鬥
out of action 出故障, 不活動, 不運轉
put into action 進入行動, 把...付諸實施
take action 採取行動, 提出訴訟

한국어 (Korean)
n. - 행동, 작용, 행위, 연기, 조처, 전투, 줄거리, 판결, 소송
v. tr. - ~을 상대로 소송을 제기하다

idioms:

bring into action 전투에 참가 시키다
go into action 행동하다
put into action 실천에 옮기다
take action 활발해지다, 조처를 취하다, 고소하다

日本語 (Japanese)
n. - 行動, 行為, 作用, 機能, 働き, 動作, 訴訟, 戦闘

idioms:

action group 市民の会, 行動委員会
action point 行動提案
action replay ビデオの即時再生
action stations 戦闘配置
evasive action 回避行動
go into action 活動を始める
out of action 活動しないで
put into action 実行に移す
take action 訴訟を起こす, 行動を取る

العربيه (Arabic)
‏(الاسم) دعوى قضائيه, تأثير, أداء, عمل, تصرف, سلوك, نشاط, معركه‏

עברית (Hebrew)
n. - ‮פעולה, מעשה, פעילות, דרך פעולה, מנגנון, תביעה משפטית, הליך משפטי, קרב, מלחמה, סידרת אירועים המוצגים בסיפור, מחזה וכו', תנועה, פקודה להתחלת הסרטת תמונה בסרט, אקשן‬
v. tr. - ‮נקט בפעולה משפטית נגד‬

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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved. Read more
		Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Read more
		Marketing Dictionary. Dictionary of Marketing Terms. Copyright © 2000 by Barron's Educational Series, Inc. All rights reserved. Read more
		Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved. Read more
		Idioms. The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company. All rights reserved. Read more
		Antonyms. © 1999-2008 by Answers Corporation. All rights reserved. Read more
		US Military Dictionary. The Oxford Essential Dictionary of the U.S. Military. Copyright © 2001, 2002 by Oxford University Press, Inc. All rights reserved. Read more
		Philosophy Dictionary. The Oxford Dictionary of Philosophy. Copyright © 1994, 1996, 2005 by Oxford University Press. All rights reserved. Read more
		Sports Science and Medicine. The Oxford Dictionary of Sports Science & Medicine. Copyright © Michael Kent 1998, 2006, 2007. All rights reserved. Read more
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action

History of term 'action'

Concepts

Mathematical definition

Disambiguation of "action" in classical physics

Action (functional)

Abbreviated action (functional)

Hamilton's principal function

Hamilton's characteristic function

Other solutions of Hamilton–Jacobi equations

Action of a generalized coordinate

Action for a Hamiltonian flow

Euler-Lagrange equations for the action integral

Example: Free particle in polar coordinates

Action principle for classical fields

Action principle in quantum mechanics and quantum field theory

Action principle and conservation laws

Modern extensions of the action principle

See also

References