Symmetry and history quantum theory: An analog of Wigner{close_quote}s theorem
- Blackett Laboratory, Imperial College, South Kensington, London SW7 2BZ (United Kingdom)
The basic ingredients of the {open_quote}{open_quote}consistent histories{close_quote}{close_quote} approach to quantum theory are a space UP of {open_quote}{open_quote}history propositions{close_quote}{close_quote} and a space D of {open_quote}{open_quote}decoherence functionals.{close_quote}{close_quote} In this article we consider such history quantum theories in the case where UP is given by the set of projectors P(V) on some Hilbert space V. We define the notion of a {open_quote}{open_quote}physical symmetry of a history quantum theory{close_quote}{close_quote} (PSHQT) and specify such objects exhaustively with the aid of an analog of Wigner{close_quote}s theorem. In order to prove this theorem we investigate the structure of D, define the notion of an {open_quote}{open_quote}elementary decoherence functional,{close_quote}{close_quote} and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT {open_quote}{open_quote}physically equivalent{close_quote}{close_quote} and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously. {copyright} {ital 1996 American Institute of Physics.}
- OSTI ID:
- 397455
- Journal Information:
- Journal of Mathematical Physics, Vol. 37, Issue 12; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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