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Different action principles have different meaning for the variations; each specific application of an action principle requires a specific Lagrangian describing the physics. A common name for any or all of these principles is "the principle of least action".
In quantum mechanics, action and quantum-mechanical phase are related via the Planck constant, and the principle of stationary action can be understood in terms of constructive interference of wave functions. In 1948, Feynman discovered the path integral formulation extending the principle of least action to quantum mechanics for electrons and ...
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Maupertuis was the first to publish a principle of least action, as a way of adapting Fermat's principle for waves to a corpuscular (particle) theory of light. [3]: 96 Pierre de Fermat had explained Snell's law for the refraction of light by assuming light follows the path of shortest time, not distance. This troubled Maupertuis, since he felt ...
Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1] Action and the variational principle are used in Feynman's formulation of quantum mechanics [ 2 ] and in general relativity. [ 3 ]
The book is a mathematical introduction to various theoretical physics concepts, such as principle of least action, Lagrangian mechanics, Hamiltonian mechanics, Poisson brackets, and electromagnetism. [3]
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The principle of virtual work, which is the form of the principle of least action applied to these systems, states that the path actually followed by the particle is the one for which the difference between the work along this path and other nearby paths is zero (to the first order).