Gravitation, geometry, and nonrelativistic quantum theory

Karel Kuchař
Phys. Rev. D 22, 1285 – Published 15 September 1980
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Abstract

In Cartan's description, classical particles freely falling in a Newtonian gravitational field follow geodesics of a curved spacetime. 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.

  • Received 15 January 1980

DOI:https://doi.org/10.1103/PhysRevD.22.1285

©1980 American Physical Society

Authors & Affiliations

Karel Kuchař

  • Department of Physics, University of Utah, Salt Lake City, Utah 84112

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Issue

Vol. 22, Iss. 6 — 15 September 1980

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