Wiener Measure Regularization for Quantum Mechanical Path Integrals
The problems associated with a regularization of quantum mechanical path integrals using continuous-time (as opposed to discrete-time) schemes are examined. All such proposals insert regularizing Wiener measures and consider the limit as the diffusion constant diverges as the final step. Two unsuccessful approaches in the Schrödinger representation are reviewed before a fairly complete treatment of the successful coherent-state representation approach is presented. Not only does the coherent-state approach provide a rigorous continuous-time regularization scheme for quantum mechanical path integrals but it also offers a natural and physically appealing formulation that is covariant under classical canonical transformations.
Unable to display preview. Download preview PDF.
- 3.S.F. Edwards, Y.V. Gulyaev: Proc. Roy. Soc. (London) A279, 229 (1964). A careful and thorough discussion of lattice regularization of path integrals in non-Cartesian coordinates is given by M. Böhm and G. Junker: “Path Integration over Compact and Non-compact Rotation Groups”, Universität Würzburg preprint, December 1986MathSciNetADSGoogle Scholar
- 7.J.R. Klauder: in Progress in Quantum /Field Theory, eds. H. Ezawa, S. Kamefuchi (North-Holland, Amsterdam, 1986), 1986), p.31Google Scholar
- 10.K. Ito: in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1961, Vol.II., p.227Google Scholar
- For a significantly improved treatment see K. Ito: in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1966, Vol.II, part 1, p.145Google Scholar
- 14.J.R. Klauder: in Path Integrals, and Their Applications in Quantum, Statistical, and Solid State Physics, eds. G.J. Papadopoulos and J.T. Devreese (Plenum Pub. Corp., 1978), p.5Google Scholar
- 17.J.R. Klauder and E.C.G. Sudarshan: Fundamentals of Quantum Optics (W.A. Benjamin Inc., New York, 1968)Google Scholar
- 20.J.R. Klauder: “Coherent-State Path Integrals for Unitary Group Representations”, to be publishedGoogle Scholar
- 22.See, e.g., M.B. Halpern: “Schwinger-Dyson Formulation of Coordinate-Invariant Regularization,” UCB-PTH-86/28 preprintGoogle Scholar