1. Fermion wave-mechanical operators in curved space-time
- Author
-
Michael Lloyd-Hart and W. J. Cocke
- Subjects
Physics ,General Relativity and Quantum Cosmology ,symbols.namesake ,Conservation law ,Angular momentum ,Classical mechanics ,Geodesic ,Dirac equation ,symbols ,Jacobi polynomials ,Eigenfunction ,Hamiltonian (quantum mechanics) ,Curved space - 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.
- Published
- 1990