Symmetries of Decoherence Functionals

Details Symmetries of Decoherence Functionals Symmetries of Decoherence Functionals

1996-07-23

arxiv.org/abs/gr-qc/9607050v1

J.Math.Phys. 38 (1997) 759-769

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to Jour.Math.Phys.; 12 pages; Latex-document

Scientific paper

10.1063/1.531889

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 $\V$. Using an analogue of Wigner's Theorem in the context of history quantum theories proven earlier, we develop the notion of a `symmetry of a decoherence functional' and prove that all such symmetries form a group which we call `the symmetry group of a decoherence functional'. We calculate---for the case of history quantum mechanics---some of these symmetries explicitly and relate them to some discussions that have appeared previously.

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