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In classical mechanics, the principle of least action states that the motion of a particle along some path always minimize the difference between its kinetic energy and its potential energy.  Mathematically, the motion of a particle always minimizes the action functional.

In classical mechanics, the principle of least action states that the motion of a particle along some path always minimize the difference between its kinetic energy and its potential energy.  Mathematically, the motion of a particle always minimizes the action functional.

In general relativity, the Least Action Principle states that the motion of a particle on a surface M must be a geodesic of M, so it must minimize the geodesic functional.

In [[General Relativity]], the Least Action Principle states that the motion of a particle on a surface M must be a geodesic of M, so it must minimize the geodesic functional.

In [[quantum mechanics]], the Least Action Principle states that the motion of a subatomic particle must minimize the [[Feynman path integral]].

In [[Quantum Mechanics]], the Least Action Principle states that the motion of a subatomic particle must minimize the [[Feynman path integral]].

Recently, mathematician Alain Connes has formulated a ''spectral action principle'' that seeks to apply the Least Action Principle to the mathematical formulation of quantum gravity.

Recently, mathematician Alain Connes has formulated a ''spectral action principle'' that seeks to apply the Least Action Principle to the mathematical formulation of quantum gravity.

[[category: physics]]

[[category: physics]]