Continuous time and consistent histories

CJ Isham*, N Linden, K Savvidou, S Schreckenberg

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

51 Citations (Scopus)


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 [C. J. Isham and N. Linden, J. Math. Phys. 36, 5392-5408 (1995)] 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 the 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. (C) 1998 American Institute of Physics. [S0022-2488(98)03304-0].

Original languageEnglish
Pages (from-to)1818-1834
Number of pages17
JournalJournal of Mathematical Physics
Issue number4
Publication statusPublished - Apr 1998



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