Fermion wave-mechanical operators in curved space-time

W. J. Cocke, Michael Lloyd-Hart

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1982-1987
Number of pages6
JournalPhysical Review D
Issue number6
StatePublished - 1990

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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