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

International Journal of Theoretical Physics (Impact Factor: 1.19). 01/1998; 37(3):995-1009. DOI: 10.1023/A:1026693218876

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.

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    ABSTRACT: The study of the field equation of arbitrary spin in Robertson-Walker space-time, previously separated by variable separation, is completed. The integration of the separated radial equations is performed in an uni-fied way with respect to the curvature parameter. Through a sequence of transformations on the variable and of the radial function, the radial equation is reported to the Heun's differential equation. The solution of the Heun's equation however does fall into the class of known func-tions such as the hypergeometric, the polynomial, the polynomial-like function, only exceptionally. Moreover the Heun's differential operator admits of a factorization, a property that would simplify the integration, only for special values of the parameters.
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