The principle of symmetric criticality
The principle of symmetric criticality
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DOI：
10.1007/bf01941322
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发表时间：
1979-10
影响因子：
2.4
通讯作者：
R. Palais
中科院分区：
文献类型：
--
作者：
R. Palais
经常显式或隐式地假设，如果变分原理在某些对称群 G 下是不变的，那么为了测试对称场配置 是否是极值，只需检查对应于同样对称的变化 ψ + δψ 的作用的第一变分的消失就足够了。我们通过例子证明这在完全普遍性上是无效的（在某些情况下它的含义甚至可能不清楚），另一方面证明了一些在相当一般的情况下验证其使用的定理（特别是如果G是一组黎曼等距，或者如果它是紧的，或者如果它是半简单的，则有一些限制）。
It is frequently explicitly or implicitly assumed that if a variational principle is invariant under some symmetry groupG, then to test whether a symmetric field configuration ϕ is an extremal, it suffices to check the vanishing of the first variation of the action corresponding to variations ϕ + δϕ that are also symmetric. We show by example that this is not valid in complete generality (and in certain cases its meaning may not even be clear), and on the other hand prove some theorems which validate its use under fairly general circumstances (in particular ifGis a group of Riemannian isometries, or if it is compact, or with some restrictions if it is semi-simple).