The Dirac equation is considered, via the Newman–Penrose formalism, in the context of the Robertson–Walker geometry. The solution of the equation, which contrary to the neutrino case is not directly separable, is reduced to the study of decoupled spatial and temporal equations. The spatial equations are explicitly integrated and show the existence of discrete energy levels in case of closed universe. Besides the neutrino, the time equation is discussed in limiting situations of the standard cosmology.

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© 1996 American Institute of Physics.
1996
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