Continuous Time and Consistent Histories

Details Continuous Time and Consistent Histories Continuous Time and Consistent Histories

1997-11-17

arxiv.org/abs/quant-ph/9711031v1

J.Math.Phys. 39 (1998) 1818-1834

Physics

Quantum Physics

Typeset in RevTeX

Scientific paper

10.1063/1.532265

We discuss the use of histories labelled by a continuous time in the approach to consistent-histories quantum theory in which propositions about the history of the system are represented by projection operators on a Hilbert space. This extends earlier work by two of us \cite{IL95} where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory. We describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about time average of the energy. We also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator. Finally, the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism.

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