Symmetry and History Quantum Theory: An analogue of Wigner's Theorem

Details Symmetry and History Quantum Theory: An analogue of Wigner's Theorem Symmetry and History Quantum Theory: An analogue of Wigner's Theorem

1996-07-23

arxiv.org/abs/gr-qc/9607051v1

J.Math.Phys. 37 (1996) 6086-6105

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

To appear in Jour.Math.Phys.; 25 pages; Latex-document

Scientific paper

10.1063/1.531765

The basic ingredients of the `consistent histories' approach to quantum theory are a space $\UP$ of `history propositions' and a space $\D$ of `decoherence functionals'. 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 `physical symmetry of a history quantum theory' (PSHQT) and specify such objects exhaustively with the aid of an analogue of Wigner's theorem. In order to prove this theorem we investigate the structure of $\D$, define the notion of an `elementary decoherence functional' 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 `physically equivalent' and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously.

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