Geometrization of Quantum Mechanics and the New Interpretation of the Scalar Product in Hilbert Space
- 11 October 1982
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 49 (15) , 1065-1068
- https://doi.org/10.1103/physrevlett.49.1065
Abstract
It is shown that the new interpretation of the scalar product in Hilbert space recently proposed by Aharanov, Albert, and Au is in fact the one underlying the stochastic phase-space formulation of nonrelativistic quantum mechanics. The extrapolation of this interpretation to the relativistic domain and its relationship to the program of geometrizing quantum theory and quantizing space-time are discussed.Keywords
This publication has 29 references indexed in Scilit:
- New Interpretation of the Scalar Product in Hilbert SpacePhysical Review Letters, 1982
- New Interpretation of the Scalar Product in Hilbert SpacePhysical Review Letters, 1981
- A self-consistent approach to quantum field theory for extended particlesFoundations of Physics, 1981
- Quantum-mechanical distribution functions: Conditions for uniquenessPhysics Letters A, 1981
- Some remarks on quantum mechanics and relativityLettere al Nuovo Cimento (1971-1985), 1980
- Consistent formulation of relativistic dynamics for massive spin-zero particles in external fieldsPhysical Review D, 1978
- Relativistic quantum kinematics on stochastic phase spaces for massive particlesJournal of Mathematical Physics, 1978
- Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spacesJournal of Mathematical Physics, 1977
- Probability measures on fuzzy events in phase spaceJournal of Mathematical Physics, 1976
- On the Quantum Correction For Thermodynamic EquilibriumPhysical Review B, 1932