2002/05/23 by Kazuo Fujikawa, Fujikawa, Kazuo
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0205239
10 pages. Published in " Fluctuating Paths and Fields", Eds. W. Janke, A. Pelster, H.J. Schmidt, and M. Bachmann (World Scientific, Singapore, 2001)
arxiv created 2002/05/23 · openalex publication_date 2002/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A general path integral analysis of the separable Hamiltonian of Liouville-type is reviewed. The basic dynamical principle used is the Jacobi's principle of least action for given energy which is reparametrization invariant, and thus the gauge freedom naturally appears. The choice of gauge in path integral corresponds to the separation of variables in operator formalism. The gauge independence and the operator ordering are closely related. The path integral in this formulation sums over orbits in space instead of space-time. An exact path integral of the Green's function for the hydrogen atom in parabolic coordinates is ilustrated as an example, which is also interpreted as one-dimensional quantum gravity with a quantized cosmological constant.