Difference between revisions of "Least Action Principle"
| Line 1: | Line 1: | ||
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 [[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. | ||
[[category: physics]] | [[category: physics]] | ||
Revision as of 01:30, March 22, 2007
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.