, Volume 37, Issue 3, pp 995-1009

Second Quantization of the Dirac Field: Normal Modes in the Robertson–Walker Space-Time

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Abstract

The quantization of the Dirac field in thecontext of the Robertson–Walker spacetime isreconsidered in some of its constitutive elements. Theparticular solutions of the Dirac equation previouslydetermined are used to construct the normal mode solutionsin the case of flat, closed, and open space-time. Theprocedure is based on a general standard definition ofinner product between solutions of the Dirac equation that is applied by making use of anintegral property of the separated time equation. Theopen-space case requires the recurrence relations offunctions associated to solutions of the Diracequation.