The geometry of the bundle of connections

Abstract

A generalized symplectic structure on the bundle of connections $p\colon C(P)\rightarrow M$ of an arbitrary principal G-bundle $\pi\colon P\rightarrow M$ is defined by means of a $p^{\ast}\mathrm{ad}P$ -valued differential 2-form $\Omega_{2}$ on C(P), which is related to the generalized contact structure on $J^{1}(P)$ . The Hamiltonian properties of $\Omega_{2}$ are also analyzed.