Fermion wave-mechanical operators in curved space-time

Journal Article · Sat Sep 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.1982· OSTI ID:6056672

Cocke, W J; Lloyd-Hart, M ^[1]

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1. Steward Observatory, University of Arizona, Tucson, Arizona 85721 (USA)

In the context of a general wave-mechanical formalism, we derive explicit forms for the Hamiltonian, kinetic energy, and momentum operators for a massive fermion in curved space-time. In the two-spinor representation, the scalar products of state vectors are conserved under the Dirac equation, but the time-development Hamiltonian is in general not Hermitian for a nonstatic metric. A geodesic normal coordinate system provides an economical framework in which to interpret the results. We apply the formalism to a closed Robertson-Walker metric, for which we find the eigenvalues and eigenfunctions of the kinetic energy density. The angular momentum parts turn out to be simpler than in the usual four-spinor representation, and the radial parts involve Jacobi polynomials.

• OSTI ID: 6056672
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 42:6; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
FERMIONS
WAVE EQUATIONS
ANGULAR MOMENTUM
DIRAC EQUATION
EIGENFUNCTIONS
EIGENVALUES
ELECTROMAGNETIC FIELDS
ENERGY DENSITY
HAMILTONIANS
KINETIC ENERGY
MASS
METRICS
POLYNOMIALS
SPACE-TIME
SPIN
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUANTUM OPERATORS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics