Path integral for the relativistic particle in curved space

Rafael Ferraro
Phys. Rev. D 45, 1198 – Published 15 February 1992
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Abstract

The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.).

  • Received 29 July 1991

DOI:https://doi.org/10.1103/PhysRevD.45.1198

©1992 American Physical Society

Authors & Affiliations

Rafael Ferraro

  • Instituto de Astronomía y Física del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
  • Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina

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Vol. 45, Iss. 4 — 15 February 1992

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