Symmetries in Constrained Systems
摘要
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any symmetry transformation can be represented as a sum of three kinds of symmetries: global, gauge, and trivial symmetries. We construct explicitly all the corresponding conserved charges as decompositions in a special constraint basis. The global part of a symmetry does not vanish on the extremals, and the corresponding charge does not vanish on the extremals as well. The gauge part of a symmetry does not vanish on the extremals, but the gauge charge vanishes on them. We stress that the gauge charge necessarily contains a part that vanishes linearly in the first-class constraints and the remaining part of the gauge charge vanishes quadratically on the extremals. The trivial part of any symmetry vanishes on the extremals, and the corresponding charge vanishes quadratically on the extremals.
引用
@article{arxiv.hep-th/0409087,
title = {Symmetries in Constrained Systems},
author = {D. M. Gitman and I. V. Tyutin},
journal= {arXiv preprint arXiv:hep-th/0409087},
year = {2007}
}
备注
The talk on Conference "Lie and Jordan algebras, their Representations and Applications II", Brazil, Guaruja, 3-8 May 2004, 9 pages, LaTex file