Least Action Principle

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 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.