# Polysymplectic reduction and the moduli space of flat connections

@article{Blacker2019PolysymplecticRA,
title={Polysymplectic reduction and the moduli space of flat connections},
author={Casey Blacker},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2019}
}
• Casey Blacker
• Published 11 October 2018
• Mathematics, Physics
• Journal of Physics A: Mathematical and Theoretical
A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate $2$-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then apply this framework to show that the moduli space $\mathcal{M}(P)$ of flat connections on a principal bundle $P$ over a compact manifold $M$ is a polysymplectic reduction of the space $\mathcal{A}(P)$ of all connections on $P$ by the action of the gauge group… Expand
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