BRST APPROACH TO HAMILTONIAN SYSTEMS A.K.Aringazin1, V.V.Arkhipov2, and A.S.Kudusov3 Department of Theoretical Physics Karaganda State University Karaganda 470074 Kazakstan Preprint KSU-DTP-10/96 Abstract BRST formulation of cohomological Hamiltonian mechanics is presented. In the path integral approach, we use the BRST gauge fixing procedure for the partition func- tion with trivial underlying Lagrangian to fix symplectic diffeomorphism invariance. Resulting Lagrangian is BRST and anti-BRST exact and the Liouvillian of classical mechanics is reproduced in the ghost-free sector. The theory can be thought of as a topological phase of Hamiltonian mechanics and is considered as one-dimensional cohomological field theory with the target space a symplectic manifold. Twisted (anti- )BRST symmetry is related to global N = 2 supersymmetry, which is identified with an exterior algebra. Landau-Ginzburg formulation of the associated d = 1, N = 2 model is presented and Slavnov identity is analyzed. We study deformations and per- turbations of the theory. Physical states of the theory and correlation functions of the BRST invariant observables are studied. This approach provides a powerful tool to investigate the properties of Hamiltonian systems. PACS number(s): 02.40.+m, 03.40.-t,03.65.Db, 11.10.Ef, 11.30.Pb. arXiv:hep-th/9811026v1 2 Nov 1998
[email protected] [email protected] [email protected] 1 1 INTRODUCTION Recently, path integral approach to classical mechanics has been developed by Gozzi, Reuter and Thacker in a series of papers[1]-[10]. They used a delta function constraint on phase space variables to satisfy Hamilton’s equation and a sort of Faddeev-Popov representation.