Finite-Dimensional Path-Summation Formulation for Quantum Mechanics
- 15 October 1973
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 8 (8) , 2503-2510
- https://doi.org/10.1103/physrevd.8.2503
Abstract
The phase-space path-summation formulation of quantum theory is reviewed. The relationships to classical mechanics, and the greater generality (as compared with the original configuration-space path-summation formulation of Feynman) are stressed. Then the formulation is extended so that one can express the transition amplitude, between states (belonging to an arbitrary basis) of a finite-dimensional quantum system (with arbitrary Hamiltonina), in path-summation form.Keywords
This publication has 11 references indexed in Scilit:
- Path Integrals and Product IntegralsJournal of Mathematical Physics, 1971
- Hamiltonian Operators via Feynman Path IntegralsJournal of Mathematical Physics, 1970
- A Path Integral for SpinPhysical Review B, 1968
- Hamiltonian Path-Integral MethodsReviews of Modern Physics, 1966
- Feynman Integrals and the Schrödinger EquationJournal of Mathematical Physics, 1964
- Hamiltonian approach to the method of summation over Feynman historiesMathematical Proceedings of the Cambridge Philosophical Society, 1963
- The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbersAnnals of Physics, 1960
- On the product of semi-groups of operatorsProceedings of the American Mathematical Society, 1959
- Transition amplitudes as sums over historiesIl Nuovo Cimento (1869-1876), 1956
- An Operator Calculus Having Applications in Quantum ElectrodynamicsPhysical Review B, 1951