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Reduction of polysymplectic manifolds

2015; Institute of Physics; Volume: 48; Issue: 5 Linguagem: Inglês

10.1088/1751-8113/48/5/055206

1751-8121

Juan Carlos Marrero, Narciso Román‐Roy, Modesto Salgado, Silvia Vilariño,

Geometry and complex manifolds

The aim of this paper is to generalize the classical Marsden–Weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure. This generalization allows us to reduce polysymplectic Hamiltonian systems with symmetries, such as those appearing in certain kinds of classical field theories. As an application of this technique, an analogue to the Kirillov–Kostant–Souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed. Our procedure corrects some mistakes and inaccuracies in previous papers (Günther 1987 J. Differ. Geom. 25 23–53; Munteanu et al 2004 J. Math. Phys. 45 1730–51) on this subject.