维基百科，自由的百科全书
根据科内利乌斯·兰佐斯的说法，任何可以用变分原理来表达的物理定律描述一种自伴的表示。这种表示也被说成是埃尔米特的，描述了在埃尔米特变换下的不变量。
菲利克斯·克莱因的爱尔兰根纲领试图鉴识这类在一组变换下的不变量。在物理学的诺特定理中，一组变换的庞加莱群（现在广义相对论中被称为规范群）定义了在一组依赖于变分原理的变换下的对称性，即作用原理。
Variational principle
From Wikipedia, the free encyclopedia
A variational principle is a scientific principle used within the calculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions. For example, to answer this question: "What is the shape of a chain suspended at both ends?" we can use the variational principle that the shape must minimize the gravitational potential energy.
According to Cornelius Lanczos, any physical law which can be expressed as a variational principle describes an expression which is self-adjoint. These expressions are also called Hermitian. Such an expression describes an invariant under a Hermitian transformation.
Felix Klein's Erlangen program attempted to identify such invariants under a group of transformations. In what is referred to in physics as Noether's theorem, the Poincaré group of transformations (what is now called a gauge group) for general relativity defines symmetries under a group of transformations which depend on a variational principle, or action principle.
According to Cornelius Lanczos, any physical law which can be expressed as a variational principle describes an expression which is self-adjoint. These expressions are also called Hermitian. Such an expression describes an invariant under a Hermitian transformation.
Felix Klein's Erlangen program attempted to identify such invariants under a group of transformations. In what is referred to in physics as Noether's theorem, the Poincaré group of transformations (what is now called a gauge group) for general relativity defines symmetries under a group of transformations which depend on a variational principle, or action principle.
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