Abstract
We consider a path integral in phase space involving a linear functional of the classical Hamiltonian and find the Schrödinger equation of which it is a propagator. Conversely, to any quantum Hamiltonian, we associate a whole family of functionals and hence of expressions of the same Schrödinger kernel; all this is carried out independently of any correspondence principle.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Feynman, R.P. and Hibbs, A.R., Quantum Mechanics and Path Integrals, Mac Graw-Hill, 1965. FeynmanR.P., Phys. Rev. 84, 10 (1951). Garrod, C., Rev. Mod. Phys. 38, 483 (1966). Blokhintsev, D.I. and Barbashov, B.M., Sov. Phys. Usp. 15, 193 (1972).
BerezinF.A., Teor. Mat. Fiz. 6, 194 (1971).
See. for example: GarczynskiW., Rep. Math. Phys. 4, 21 (1973). Truman, A., J. Math. Phys. 17, 1852 (1976). Combe, Ph., Rideau, G., Rodriguez, R., and Sirugue-Collin, M., Preprint CPT (Marseilles), 1976. Mizrahi, M.M., J. Math. Phys. 19, 298 (1978). and references cited therein.
Witt-MoretteC.de, et al., Gen. Rel. Grav. 8, 581 (1977).
CohenL., J. Math. Phys. 17, 597 (1976).
TestaF.J., J. Math. Phys. 12, 1471 (1971). Dowker, J.S., J. Math. Phys. 17, 1873 (1975). Sato, M., Prog. Theor. Phys. 58, 1262 (1977). Leschke, H., and Schmutz, M., Z. Physik B 27, 85 (1977).
MizrahiM.M., J. Math. Phys. 16, 2201 (1975).
FanelliR., J. Math. Phys. 17, 490 (1976).
MayesI.W., and DowkerJ.S., J. Math. Phys. 14, 434 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bertrand, J., Irac, M. Non-uniqueness in writing Schrödinger kernel as a functional integral. Lett Math Phys 3, 97–107 (1979). https://doi.org/10.1007/BF00400063
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00400063