The principle of least action was first formulated by Pierre-Louis Moreau de Maupertuis, who said that "Nature is thrifty in all its actions". See action (physics). Others who developed the idea included Euler and Leibniz. It should be said that, from the point of view of the calculus of variations, principle of stationary action is more accurate.
The principle of least action led to the development of the Lagrangian and Hamiltonian formulations of classical mechanics. Although they are at first more difficult to grasp, they have the advantage that their world-view is more transferable to the frameworks of relativistic and quantum-mechanical physics than that of Newton's laws.
This has caused some people to think that this principle is a "deep" principle of physics.
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.
In physics, the principle of leastaction or principle of stationary action is a variational principle by which, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system.
The principle remains central in modern physics and mathematics, being applied in the theory of relativity, quantum mechanics and quantum field theory, and a focus of modern mathematical investigation in Morse theory.
By contrast, the actionprinciple is not localized to a point; rather, it involves integrals over an interval of time and (for fields) extended region of space.
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