Quantum canonical transformations as integral transformations
- 15 April 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 25 (8), 2103-2117
- https://doi.org/10.1103/physrevd.25.2103
Abstract
We discuss how the Hamiltonian changes in quantum canonical transformations. To the operator one can associate (in a given ordering rule) a -number function . It is this function that appears in the action of the phase-space path integral. A quantum canonical transformation can now be expressed as an integral transformation . The kernel is constructed explicitly for point transformations and for the , reflection by studying changes of variables in the path integral. The ordering dependence of is displayed. The invariance of commutation rules is also discussed.
Keywords
This publication has 24 references indexed in Scilit:
- Functional integration through inverse scattering variables. IIPhysical Review D, 1980
- Functional integration through inverse scattering variablesPhysical Review D, 1980
- Definition of path integrals and rules for non-linear transformationsNuclear Physics B, 1978
- Point canonical transformations in the path integralNuclear Physics B, 1976
- Canonical functional integrals in general coordinatesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1972
- Path Integrals in Curved SpacesJournal of Mathematical Physics, 1971
- Feynman's kernel and the classical pathMathematical Proceedings of the Cambridge Philosophical Society, 1965
- Path integrals in polar co-ordinatesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1964
- Hamiltonian approach to the method of summation over Feynman historiesMathematical Proceedings of the Cambridge Philosophical Society, 1963
- Dynamical Theory in Curved Spaces. I. A Review of the Classical and Quantum Action PrinciplesReviews of Modern Physics, 1957