Symmetries of decoherence functionals

Journal Article · Sat Feb 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531889· OSTI ID:466874

Schreckenberg, S ^[1]

---

1. Blackett Laboratory, Imperial College, South Kensington, London SW7 2BZ (United Kingdom)

The basic ingredients of the {open_quotes}consistent histories{close_quotes} approach to quantum theory are a space scr(UP) of {open_quotes}history propositions{close_quotes} and a space scr(D) of {open_quotes}decoherence functionals.{close_quotes} In this article we consider such history quantum theories in the case where scr(UP) is given by the set of projectors scr(P)(scr(V)) on some Hilbert space scr(V). Using an analog of Wigner{close_quote}s theorem in the context of history quantum theories proven earlier, we develop the notion of a {open_quotes}symmetry of a decoherence functional{close_quotes} and prove that all such symmetries form a group which we call {open_quotes}the symmetry group of a decoherence functional.{close_quotes} We calculate for the case of standard quantum mechanics{emdash}when looked at from the perspective of the history program{emdash}some of these symmetries explicitly and relate them to some discussions that have appeared previously. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 466874
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLASSIFICATION
FUNCTIONALS
HILBERT SPACE
QUANTUM MECHANICS
SCHROEDINGER PICTURE
SYMMETRY