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Topic: Principle of stationary action

	Action (physics) - Wikipedia, the free encyclopedia
		In physics, the action is an integral quantity that is used to determine the evolution of a physical system between two defined states using the calculus of variations.
		The action is usually an integral over time, but may be integrated over spatial variables as well (for action pertaining to fields); in still other cases, the action is integrated along the path followed by the physical system.
		The action corresponding to the various paths is used to calculate the path integral, that gives the probability amplitudes of the various outcomes.
	en.wikipedia.org /wiki/Action_(physics) (1697 words)

	Dynamics - LoveToKnow 1911
		- The fundamental principles of dynamics, and their application to special problems, are explained in the articles Mechanics and Motion, Laws Of, where brief indications are also given of the more general methods of investigating the properties of a dynamical system, independently of the accidents of its particular constitution, which were inaugurated by J. Lagrange.
		The " action " of a single particle in passing from one position to another is the space-integral of the momentum, or the time-integral of the vis viva.
		Before leaving this topic the connexion of the principle of stationary action with a well-known theorem of optics may be noticed.
	www.1911encyclopedia.org /Dynamics (9175 words)

	The Action Unit as a Primary Unit in the SI
		In conclusion, action, in the opinion of the author, deserves to be assigned a specific measurement unit, also because it plays, in physics, the same unifying role, as that recognized by Giorgi in the joule (or the watt), towards the establishment of a coherent, rational system of units.
		that action is a scalar describing change, which has the same value for all inertial observers, no matter how high is their relative speed of motion or (which is the same) their speed relative to the observed object.
		Hence, action is the fundamental invariant describing any kind of change in the outer world of the observer, much the same as information is the fundamental invariant describing change in the inner world (mind) of the observer.
	www.cartage.org.lb /en/themes/Sciences/Physics/Mechanics/Lagrangian/Actionunit/Actionunit.htm (2572 words)

	mp_arc 01-166 (Site not responding. Last check: 2007-11-05)
		For an arbitrary holonomic mechanical system a method for constructing time-discrete trajectories is derived by applying a generalized principle of stationary action to the manifold of those system paths which are parabolic with respect to system of generalized coordinates.
		The method is applied to the anti-damped harmonic oscillator, and data are reported that suggest that the method accurately represents the growth of the amplitude till numerical overflow.
		A modified variational derivative of the generalized action integral is shown to agree with the force that the environment of the system exerts to it.
	www.ma.utexas.edu /mp_arc-bin/mpa?yn=01-166 (119 words)

	outcome counting, the action principle, and GR
		QFT ==> action principle ==> GR Firstly, QM was created by quantizing Hamiltonian mechanics, so it is no surprise that the FPI approach, which is analogous to Schrodinger/Heisenberg mechanics (as proved by Feynman), yields the principle of stationary action.
		Of course, the principle of stationary action was designed (years before QM) to yield Newtonian mechanics (in most cases).
		I understand that Feynman recovered the path action principle in the QM of particles, but I'm still confused where exactly the action principle appears in QFT, ie whether it is assumed or recovered (as you say) from something else...
	www.physicsforums.com /showthread.php?p=935779 (1900 words)

	Principle Voices - Polygamy Versus Democracy: You Can't Have Both
		Their goal is to establish the principle that individuals have the right to create and define their families as they see fit.
		Francis Lieber's idea that certain social practices "fetter a people in stationary despotism" was widely shared at the time, and resonates with our contemporary interest in democracy promotion.
		MRAP threatened to bring legal action against the historian HÃ©lÃ¨ne CarrÃ¨re d'Encausse, permanent secretary of the prestigious French Academy, for her suggestion that large families with little parental supervision crammed into small apartments had played a role in the disturbances.
	www.principlevoices.org /article.php?story=20060603222031984 (6674 words)

	Fermat's Principle -- from Eric Weisstein's World of Physics
		The original statement of Fermat's principle was, "The actual path between two points taken by a beam of light is the one which is traversed in the least time." Snell's law and the law of reflection follow directly from this statement.
		It may be reformulated slightly in terms of optical path length as "Light, in going between two points, traverses the route having the smallest optical path length." In its original form however, Fermat's principle is somewhat incomplete and even slightly in error.
		Its modern form is "A light ray, in going between two points, must traverse as optical path length which is stationary with respect to variations of the path." In this formulation, the paths may be maxima, minima, or saddle points.
	scienceworld.wolfram.com /physics/FermatsPrinciple.html (140 words)

	National Call To Action To Promote Oral Health
		Rather, just as the actions have been developed through a process of collaboration and communication across public and private domains, their successful execution calls for partnerships that unite private and public groups focused on common goals.
		The five actions outlined in this report require public-private partnerships at all levels of society and a commitment from those who are involved in health programs to contribute expertise and resources.
		On the principle of strength through numbers, coalitions of such groups, especially partnering oral health patient organizations with medical disease organizations (e.g., heart, cancer, diabetes, arthritis) might achieve a greater impact, while underscoring that oral health and general health are inextricably linked.
	www.surgeongeneral.gov /topics/oralhealth/nationalcalltoaction.htm (12123 words)

	Richard Feynman
		Feynman's thesis applied the principle of stationary action to problems of quantum mechanics, laying the groundwork for the "path integral" approach and Feynman diagrams.
		As a junior physicist, his work on the project was relatively removed from the major action, consisting mostly of administering the computation group of human computers in the Theoretical division, and then, with Nicholas Metropolis, setting up the system for using IBM punch cards for computation.
		His principle was that if a topic could not be explained in a freshman lecture, it was not fully understood yet.
	www.jewishvirtuallibrary.org /jsource/biography/feynman.html (2011 words)

	The Animated Cartoon Factory - Animation Basics
		The Stationary Seaweed is another form of the overlapping action principle.
		A practical application of this would be the tail of a dog wagging or a pony tail on a girl as she runs.
		The action of the line is contained to a finite area as opposed to the wider swing of the pendulum.
	www.brianlemay.com /animationexamples/stationaryseaweed.html (217 words)

	Principle of least action - Wikipedia, the free encyclopedia
		Credit for the formulation of the principle of least action is commonly given to Pierre Louis Maupertuis, who wrote about it in 1744
		Maupertuis' priority was disputed in 1751 by the mathematician Samuel König, who claimed that it had been invented by Gottfried Leibniz in 1707.
		applied the variational principle to the function L = T − V to obtain what are now called the Lagrangian equations of motion.
	en.wikipedia.org /wiki/Principle_of_least_action (1500 words)

	Theory of Atoms in Molecules: Quantum Mechanics of a Proper Open System
		Thus the statement of the principle of stationary action for a proper open system is simply a generalization of quantum mechanics that applies to all physical systems.
		The operational statement of this theory is most elegantly and simply stated using the language of field theory.
		This force is equated to the sum of a basin and a surface contribution: the basin contribution is the commutator average and the surface term is the momentum flux through the surface, a term described by the quantum stress tensor
	www.chemistry.mcmaster.ca /faculty/bader/aim/aim_4.html (914 words)

	Narlikar's "Creation" of the Big Bang Universe Was a Mere Origination
		But let us note that even an unrestricted conservation principle does not rule out a cosmological model featuring a first moment of time, that is, a model featuring an instant that has no temporal predecessor.
		Narlikar apparently overlooked my subjunctive conditional clause "if the principle of conservation of energy or mass-energy were to have [temporally and cosmologically unrestricted] validity." Clearly, I was merely calling attention to the incompatibility of the putatively unrestricted conservation principle with creation ex nihilo, and to its own logical compatibility with a bounded finite past.
		Narlikar proposes to banish t = 0 as a singularity at which the time axis is terminated by considering it "as a defect of the classical gravity theory" (1992, 365), arising from "an incomplete understanding of how gravity operates when matter is in an extremely dense state" (1988, 67; 1992, 370).
	www.infidels.org /library/modern/adolf_grunbaum/narlikar.html (3412 words)

	Time Travel Portal :: View topic - Closed Timelike Curves, Time Machines and Black Hole Collisions (Site not responding. Last check: 2007-11-05)
		We consider the action principle to derive the classical, non-relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves.
		Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action by A. Carlini, V. Frolov, M. Mensky, I. Novikov and H. Soleng.
		We consider the action principle to derive the classical, relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves.
	timetravelportal.com /viewtopic.php?t=626 (1810 words)

	Reproducibility (Site not responding. Last check: 2007-11-05)
		de: Nachvollziehbarkeit Reproducibility is one of the main principles of the scientific method.
		An experimental description (thought experiment) produced by a particular researcher or group of researchers is generally evaluated by other independent researchers by attempting to reproduce it; they repeat the same experiment themselves and see if it gives equal results as reported by the original group.
		Because reproducibility of thought-experimental definitions, algorithms such as recipes, and of results obtained in their application allows them to be communicated, there is tendency to remove redundancy or elaboration in scientific writing in favor of giving exhaustive citations.
	www.keywordmage.net /re/reproducibility.html (241 words)

	Special topic course
		Classical case: Hamiltonian actions of symmetry groups on a state space.
		Group symmetry of the action functional and conservation laws.
		Action of the Poincare group on spinor fields.
	www.math.ttu.edu /~vshubov/outline_quantum.html (518 words)

	Theory of Atoms in Molecules: The Topological Atom is the Quantum Atom
		Schwinger's generalization of the action principle, as contained in his principle of stationary action, in addition to determining the field equation, yields a variational derivation of Heisenberg's equation of motion for any observable
		Thus a single principle of physics determines the properties of the total system and its constituent atoms.
		The properties of the topological atoms coincide with those ascribed to the atoms of chemistry; (i) they are additive to yield the corresponding property for the total system and (ii) they are transferable from one system to another to the extent that the transfer leaves their distribution of charge unchanged.
	www.chemistry.mcmaster.ca /faculty/bader/aim/aim_3.html (791 words)

	What is the ACTION?
		I have understood that a body moves in a geodesic of curved space-time according to the maximum proper time and this is equivalent to follow the minimum-action path.
		Yes - the action is the proper time expressed in different variables.
		Part of the Lagrangain formalism is to find the value of the function L in terms of the variabes t,x,dx/dt, i.e.
	www.physicsforums.com /showthread.php?threadid=135805 (543 words)

	A The longitudinal character of the scalar wave in the field gravity theory (Site not responding. Last check: 2007-11-05)
		To derive the equation of motion for test particles in the frame of the field gravity theory we start from the stationary action principle in the form
		where the variation of the action is made with respect to the particle trajectories
		(A.19) under the action of the scalar gravitational wave a test mass undergo small longitudinal oscillations in the direction of wave propagation (z-axis):
	aanda.u-strasbg.fr:2002 /papers/aa/full/2001/19/aa9919/node7.html (687 words)

	NONLINEAR SEISMIC ANALYSIS OF ARCH DAMS USING SLIP-JOINT ELEMENTS
		The equality of the total linear impulse and change in linear momentum, and the equality of total angular impulse and change in angular momentum, assuming elastic, frictionless contact, are applied to each body.
		To completely define elastic impact the conservation of kinetic energy principle is applied to the two bodies as a single system.
		The terms involving the x and z components of velocity of the bodies have been deleted from the energy expression as they are unchanged by the impact.
	www.public.asu.edu /~avixx/Documents/techequ/techequ.htm (5988 words)

	Re: principle of least action (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-05)
		The book also does an excellent job of introducing the intuition behind the Principle of Stationary Action (there must be a better name.
		After this you could move on to an electron moving in a field and show that the path is curved.
		He also declared the class to be a failure at its ostensible goal, that of teaching freshmen and sophomores.
	www.lns.cornell.edu.cob-web.org:8888 /spr/2004-06/msg0061661.html (312 words)

	March 2006 Updates
		We are on the point of being able to see the effects of our actions and their probable consequences in the future; we hold the future still timidly, but perceive it for the first time, as a function of our own action.
		The field equations obtained from the Hilbert-Einstein action by varying the w^ab_u are algebraic in the w^ab_u...
		The classical solution, corresponding to the principle of stationary action, may be taken to be the de Sitter universe...
	www.valdostamuseum.org /hamsmith/Mar2006Update.html (16800 words)

	Hamilton's Principle -- from Eric Weisstein's World of Physics
		Hamilton's Principle -- from Eric Weisstein's World of Physics
		has a stationary value for the correct path of motion, where L is the Lagrangian, so
		A modified version of Hamilton's principle states that
	scienceworld.wolfram.com /physics/HamiltonsPrinciple.html (33 words)

	Lagrangian - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-05)
		The same principle, and the Lagrange formalism, are tied closely to Noether's Theorem, which relates physical conserved quantities to continuous symmetries of a physical system; and Lagrangian mechanics and Noether's Theorem together yield a natural formalism for first quantization by including commutators between certain terms of the Lagrangian equations of motion for a physical system.
		In order for the action to be local, we need additional restrictions on the action.
		Incidentally, the left hand side is the functional derivative of the action with respect to φ.
	en.wikipedia.org.cob-web.org:8888 /wiki/Lagrangian (1001 words)

	Re: principle of least action (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-05)
		After this you > could move on to an electron moving in a field and show that the path > is curved.
		Whoever thinks MOST Freshmen/Sophomores are ready to tackle Lagrange Multipliers and variational calulus when many of them are being introduced to blocks sliding down inclined planes and frictionless pulleys for the first time you can be my guest to see your student evaluations at the end of the term of teaching!
		Anyway is not the principle of least action just another statement of the fact that a body will travel a geodesic in its traveling between two points for the energy momentum tensor of the correct geometry of the space-time containing the points?
	www.lns.cornell.edu.cob-web.org:8888 /spr/2004-06/msg0061709.html (578 words)

	Tutorial Topics (Site not responding. Last check: 2007-11-05)
		Examples of the concepts from differential geometry that we will study include symplectic forms, which arose from the Hamiltonian formulation of mechanics.
		Another example is the principle of stationary action, which comes from basic Langrangian mechanics and which leads to the study of geodesics on a Riemannian manifold.
		As an example of the theorems that we will study, there is Liouville's theorem, which states that the volume of a region in the phase space of a Hamiltonian system is invariant under time.
	www.math.harvard.edu /undergrad/Pamphlets/tutorial_01_02.html (497 words)

	Predicting Classical Motion Directly from the Action Principle III (ResearchIndex) (via CobWeb/3.1 ... (Site not responding. Last check: 2007-11-05)
		Predicting Classical Motion Directly from the Action Principle III
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Abstract: For an arbitrary holonomic mechanical system a method for constructing time-discrete trajectories is derived by applying a generalized principle of stationary action to the manifold of those system paths which are parabolic with respect to system of generalized coordinates.
	citeseer.ist.psu.edu.cob-web.org:8888 /545732.html (291 words)

	The Cosmological Argument: The First Cause or Prime Mover (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-11-05)
		This Article shows how this is not the case by pursuing a novel approach wherein it is understood that an infinite set of real entities is not a set, considered as a technical term of art, within the meaning of Cantorian theory.
		This article will appeal to those readers (especially those who accept the principle that there must be a cause for whatever begins to exist) who think that there is something to the Kalam Cosmological Argument that has not as yet been satisfactorily answered by its critics.
		When applied to the beginning of time, the principle that whatever begins to exist must have a cause is not clearly true.
	www.infidels.org.cob-web.org:8888 /library/modern/theism/cosmological.html (3646 words)

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