Abstract
The structure of the history phase space 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 includes the time map from the spacetime manifold (the two-sheet) to a one-dimensional time manifold as one of its configuration variables. A canonical history action is posited on 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 The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices of foliating The history Poisson brackets of spacetime fields on induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms and temporal diffeomorphisms Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space 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