From the principle of stationary action, the Yang Mills equations follow.
2.
Maupertuis'principle and Hamilton's principle exemplify the principle of stationary action.
3.
The principle of stationary action states that the action is stationary with respect to variations of coordinates that leave the endpoints of the trajectory fixed.
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In fact, the spin of matter in curved spacetime requires that torsion is not constrained to be zero but is a variable in the principle of stationary action.
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In quantum mechanics, phase are related via Planck's constant, and the principle of stationary action can be understood in terms of constructive interference of wave functions.
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From a theoretical viewpoint, field equations can be formulated in the frameworks of Lagrangian field theory, Hamiltonian field theory, and field theoretic formulations of the principle of stationary action.
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In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler Lagrange equation for the field.
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The basic principle of Lagrangian mechanics, the principle of stationary action, is that an object subjected to outside influences will " choose " a path which makes a certain quantity, the " action ", an extremum.
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