Difference between revisions of "Least Action Principle"
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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 | + | 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 [[ | + | 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]] | ||
Revision as of 01:31, 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.