Research in Engineering and Aviation

New Formulation of the Classical Path Integral with Reparameterization Invariance

January 1997

Author(s): Thacker, W.D.

Journal: Journal of Mathematical Physics, Vol. 38, pp.2389-2416 (1997). DOI: 10.1063/1.531987


A classical path integral (CPI) provides a functional integral representation of the kernel which propagates phase space density distributions. In this paper a new formulation of the CPI is developed in which time and energy are promoted to dynamical variables. The reparametrization invariance, inherent in this formalism, is handled by means of the Batalin–Fradkin–Vilkovisky method. The path integral action possesses a set of ISp(2) symmetries connected with reparametrization invariance and an additional set of ISp(2) symmetries connected with the symplectic geometry of the extended phase space. Supersymmetry is also present in the CPI action. This formulation of the CPI allows us to study the dependence on energy of the dynamical evolution of Hamiltonian systems. It naturally incorporates the constraints onto the energy surface.