Polysymplectic reduction and the moduli space of flat connections
Abstract
A polysymplectic structure is a vectorvalued symplectic form, that is, a closed nondegenerate 2form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space [ image ], we then apply this framework to show that the moduli space of flat connections on a principal bundle over a compact manifold M is a polysymplectic reduction of the space of all connections by the action of the gauge group with respect to a natural polysymplectic structure with values in an infinite dimensional Banach space. As a consequence, the moduli space inherits a canonical H^{2}(M)valued presymplectic structure.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 August 2019
 DOI:
 10.1088/17518121/ab2eed
 arXiv:
 arXiv:1810.04924
 Bibcode:
 2019JPhA...52G5201B
 Keywords:

 polysymplectic geometry;
 Hamiltonian reduction;
 moment maps;
 gauge theory;
 Mathematics  Differential Geometry;
 53D05;
 53D20;
 53D30;
 70S15
 EPrint:
 38 pages