Stress–energy–momentum tensors for natural constrained variational problems

✍ Scribed by A. Fernández; P.L. Garcı́a; C. Rodrigo

• Book ID: 104343241
• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 175 KB
• Volume: 49
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(03)00058-5

✦ Synopsis

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.