The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe
arXiv:0901.0602 · doi:10.1088/0264-9381/26/10/105021
Abstract
We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a space-time normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form.
22 pages, LaTeX, sign error in equation (3.7) corrected