Reduction of polysymplectic manifolds

Abstract

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 in- herit 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 analogous 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 [29, 50] on this subject.

Latex file. 33 pages. New examples, comments and references are added

References in corpus (7)

• Linear and multiplicative 2-forms
• Multi-moment maps
• Closed forms and multi-moment maps
• Routhian reduction for quasi-invariant Lagrangians
• Euler-Poincare reduction for discrete field theories
• On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
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Cited by in corpus (14)

• Reduction of multisymplectic manifolds
• Remarks on multisymplectic reduction
• Quantization of Polysymplectic Manifolds
• Polysymplectic Reduction and the Moduli Space of Flat Connections
• On k-polycosymplectic Marsden-Weinstein reductions
• Poisson-Poincaré reduction for Field Theories
• Symmetry reduction, integrability and reconstruction in k-symplectic field theory
• Cosymplectic geometry, reductions, and energy-momentum methods with applications
• Routh reduction for first-order field theories
• Poly-Poisson Sigma models and their relational poly-symplectic groupoids
• Conditions for symmetry reduction of polysymplectic and polycosymplectic structures
• Cotangent bundle reduction and Routh reduction for polysymplectic manifolds
• An energy-momentum method for ordinary differential equations with an underlying $k$-polysymplectic manifold
• Multisymplectic observable reduction using constraint triples