### Abstract

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 language | English (US) |
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Pages (from-to) | 1982-1987 |

Number of pages | 6 |

Journal | Physical Review D |

Volume | 42 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jan 1 1990 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*42*(6), 1982-1987. https://doi.org/10.1103/PhysRevD.42.1982