Gravitation, geometry, and nonrelativistic quantum theory

Journal Article · Mon Sep 15 04:00:00 EDT 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.22.1285· OSTI ID:5054530

Kuchar, K

In Cartan's description, classical particles freely falling in a Newtonian gravitational field follow geodesics of a curved space-time. We cast this geodesic motion into generalized Hamiltonian form and quantize it by Dirac's constraint method in a coordinate-independent way. The Dirac constraint takes a simplified form in special noninertial frames (nonrotating, rigid, Galilean, and Gaussian). Transformation theory of the state function allows us to compare descriptions of a given quantum state by two different observers and to illustrate how the principle of equivalence works for quantum systems. In particular, we show that quantum states of a particle moving in a homogeneous gravitational field and of the gravitational harmonic oscillator can be reduced to the study of plane waves in an appropriate frame.

• Research Organization: Department of Physics, University of Utah, Salt Lake City, Utah 84112
• OSTI ID: 5054530
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 22:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUIVALENCE PRINCIPLE
FIELD THEORIES
GEODESICS
GRAVITATIONAL FIELDS
HAMILTONIANS
HARMONIC OSCILLATOR MODELS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SPACE-TIME
WAVE EQUATIONS