Reduction of multisymplectic manifolds

Abstract

We extend the Marsden-Weinstein-Meyer symplectic reduction theorem to the setting of multisymplectic manifolds. In this context, we investigate the dependence of the reduced space on the reduction parameters. With respect to a distinguished class of multisymplectic moment maps, an exact stationary phase approximation and nonabelian localization theorem are also obtained.

arXiv comment31 pages

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Cited by in corpus (13)

• Multicontact formulation for non-conservative field theories
• Contact Lie systems
• More insights into symmetries in multisymplectic field theories
• Homotopy momentum sections on multisymplectic manifolds
• Poisson-Poincaré reduction for Field Theories
• On k-polycosymplectic Marsden-Weinstein reductions
• Monge-Ampere Geometry and Vortices
• Coisotropic reduction in Multisymplectic Geometry
• Graded Poisson and Graded Dirac structures
• Brackets in multicontact geometry and multisymplectization
• Cotangent bundle reduction and Routh reduction for polysymplectic manifolds
• Reduction and reconstruction of multisymplectic Lie systems
• Multisymplectic observable reduction using constraint triples