Path integrals for a particle in curved space

Journal Article · Mon Jan 15 04:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.438· OSTI ID:6382508

Parker, L

We consider a particle obeying the Schroedinger equation in a general curved n-dimensional space, with arbitrary linear coupling to the scalar curvature of the space. We give the Feynman path-integral expressions for the probability amplitude, , for the particle to go from x' to x in time s. This generalizes results of DeWitt, Cheng, and Hartle and Hawking. We show in particular, that there is a one-parameter family of covariant representations of the path integral corresponding to a given amplitude. These representations are different in that the covariant expressions for the incremental amplitudes, , appearing in the definition of the path integral, differ even to first order in epsilon (after dropping common factors). Finally, using the proper-time representation, we give the corresponding generally covariant expressions for the propagator of a scalar field with arbitrary linear coupling to the scalar curvature of the spacetime.

• Research Organization: Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
• OSTI ID: 6382508
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COUPLING CONSTANTS
DIFFERENTIAL EQUATIONS
EQUATIONS
FEYNMAN PATH INTEGRAL
INTEGRALS
PARTICLE KINEMATICS
PROBABILITY
PROPAGATOR
SCALAR FIELDS
SCHROEDINGER EQUATION
SPACE-TIME
WAVE EQUATIONS