Reduction of Presymplectic Manifolds with Symmetry

Details Reduction of Presymplectic Manifolds with Symmetry Reduction of Presymplectic Manifolds with Symmetry

1999-11-05

arxiv.org/abs/math-ph/9911008v1

Rev. Math. Phys. 11(10) (1999) 1209-1247

Physics

Mathematical Physics

36 pages. LaTeX file. To be published in Reviews in Mathematical Physics

Scientific paper

Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a method of reduction which enables us to remove gauge symmetries as well as non-gauge ``rigid'' symmetries at once. This method is compared with other step-by-step reduction procedures. As particular examples in this framework, we discuss the reduction of time-dependent dynamical systems with symmetry, the reduction of a mechanical model of field theories with gauge and non-gauge symmetries, and the gauge reduction of the system made of a conformal particle.

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