Constrained systems, generalized Hamilton-Jacobi actions, and quantization

Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In classical theory, infinite-dimensional targets considered as well (this then encompasses also higher-dimensional theories in hamiltonian formalism). The properties Hamilton–Jacobi (HJ) action described details and several examples explicitly computed (including nonabelian Chern–Simons where HJ turns out to be gauged Wess–Zumino–Witten action). Perturbative quantization, limited note finite-dimensional targets, is performed framework Batalin–Vilkovisky (BV) formalism bulk Batalin–Fradkin–Vilkovisky (BFV) at endpoints. As a sanity check method, it proved that semiclassical contribution physical part evolution operator still given by action. Several explicitly. particular, shown toy model for theory 7D nonlinear Hitchin polarization do not have quantum corrections (the extension these results actual cases discussed companion paper [21]). Background material both (symplectic geometry, generalized generating functions, actions, concepts manifolds) (BV-BFV formalism) provided.