Symmetry and history quantum theory: An analog of Wigner{close_quote}s theorem

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531765· OSTI ID:397455

Schreckenberg, S ^[1]

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1. 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, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
FUNCTIONALS
HILBERT SPACE
QUANTUM MECHANICS
SYMMETRY