Quantum Logic and the Histories Approach to Quantum Theory

Details Quantum Logic and the Histories Approach to Quantum Theory Quantum Logic and the Histories Approach to Quantum Theory

1993-08-09

arxiv.org/abs/gr-qc/9308006v1

J.Math.Phys. 35 (1994) 2157-2185

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

TP/92-93/39 36 pages + one page of diagrams (I could email Apple laser printer postscript file for anyone who is especially ke

Scientific paper

10.1063/1.530544

An extended analysis is made of the Gell-Mann and Hartle axioms for a generalised `histories' approach to quantum theory. Emphasis is placed on finding equivalents of the lattice structure that is employed in standard quantum logic. Particular attention is given to `quasi-temporal' theories in which the notion of time-evolution is less rigid than in conventional Hamiltonian physics; theories of this type are expected to arise naturally in the context of quantum gravity and quantum field theory in a curved space-time. The quasi-temporal structure is coded in a partial semi-group of `temporal supports' that underpins the lattice of history propositions. Non-trivial examples include quantum field theory on a non globally-hyperbolic spacetime, and a simple cobordism approach to a theory of quantum topology. It is shown how the set of history propositions in standard quantum theory can be realised in such a way that each history proposition is represented by a genuine projection operator. This provides valuable insight into the possible lattice structure in general history theories, and also provides a number of potential models for theories of this type.

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