Stress–energy–momentum tensors for natural constrained variational problems
- 作者：Ferná ; ndez ; A. ; Garcí ; a ; P.L. ; Rodrigo ; C.
- 关键词：58E30 ; 76M30 ; 83C40 ; Natural Lagrangian densities ; Poincaré ; &ndash ; Cartan forms ; Multi-momentum maps ; Stress&ndash ; energy&ndash ; momentum tensors
- 刊名：Journal of Geometry and Physics
- 出版年：2004
- 期刊代码：29_03930440
- 类别：ph
- 出版时间：January, 2004
- 卷：49
- 期：1
- 页码：1-20
- 文件大小：175 K
摘要
Under certain parameterization conditions for the “infinitesimal admissible variations”, we propose a theory for constrained variational problems on arbitrary bundles, which allows us to introduce in a very general way the concept of multi-momentum map associated to the infinitesimal symmetries of the problem. For natural problems with natural parameterization, a stress–energy–momentum tensor is constructed for each “admissible section” from the multi-momentum map associated to the natural lifting of vector fields on the base manifold. This tensor satisfies the typical properties of a stress–energy–momentum tensor (Diff(X)-covariance, Belinfante–Rosenfeld type formulas, etc.), and also satisfies corresponding conservation and Hilbert type formulas for natural problems depending on a metric. The theory is illustrated with several examples of geometrical and physical interest.