Diffeomorphisms as symplectomorphisms in history phase space: Bosonic string model

I. Kouletsis and K. V. Kuchař
Phys. Rev. D 65, 125026 – Published 19 June 2002
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Abstract

The structure of the history phase space G of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space G includes the time map T from the spacetime manifold (the two-sheet) Y to a one-dimensional time manifold T as one of its configuration variables. A canonical history action is posited on G such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on G. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices T of foliating Y. The history Poisson brackets of spacetime fields on G induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space G0 of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms DiffY and temporal diffeomorphisms DiffT. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space G. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model.

  • Received 13 August 2001

DOI:https://doi.org/10.1103/PhysRevD.65.125026

©2002 American Physical Society

Authors & Affiliations

I. Kouletsis* and K. V. Kuchař

  • Department of Physics, University of Utah, Salt Lake City, Utah 84109

  • *Present address: Institut für theoretische Physik, Universität Bern, CH-3012 Bern, Switzerland.

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Vol. 65, Iss. 12 — 15 June 2002

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