- Authors:
- DOI:
- 10.1016/0034-4877(84)90008-9
- Abstract:
- A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered distribution. We show that h is in the domain of a generalized Weyl map and define Exp0(-h) as a tempered distribution provided h satisfies a certain semi-boundedness condition. The condition given is linear in h; it coincides with usual boundedness from below if h depends only on one canonical variable. Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations of the twisted structure is added
- Type:
- Journal article
- Language:
- English
- Published in:
- Reports on Mathematical Physics, 1984, Vol 19, Issue 3, p. 361-381
- Main Research Area:
- Social science
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 1984
- Scientific Level:
- Scientific
- ID:
- 28227064
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