The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe

Details The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe The Dirac Equation and the Normalization of its Solutions in a Closed Friedmann-Robertson-Walker Universe

2009-01-06

arxiv.org/abs/0901.0602v3

Class.Quant.Grav. 26 (2009) 105021

Physics

Mathematical Physics

22 pages, LaTeX, minor corrections (published version)

Scientific paper

10.1088/0264-9381/26/10/105021

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.

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