Article
Second Quantization of the Dirac Field: Normal Modes in the Robertson–Walker SpaceTime
Department of Physics, University of Milan, Milano, Lombardy, Italy
International Journal of Theoretical Physics
(Impact Factor: 1.19).
03/1998;
37(3):9951009.
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 spacetime. 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. Theopenspace case requires the recurrence relations offunctions associated to solutions of the Diracequation.

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ABSTRACT: The spinor formulation of the massive spin1 equation is considered in the general RobertsonWalker spacetime. The corresponding differential equations are separated by an elementary separation method that has the advantage of being a simple extension of the one previously used in the massless case. The independent separated angular and radial equations are shown to reduce to those of the massless case and are explicitly integrated. Two separated time functions satisfying two coupled differential equations are necessary to describe the time dependence. Explicit solutions of the time equations are given in the massless case and for some meaningful laws of universe expansion in the massive case.Il Nuovo Cimento B 05/2005; 120(5). DOI:10.1393/ncb/i2005100587 
Article: The EinsteinDirac Equation in RobertsonWalker SpaceTime Does Not Admit Standard Solutions
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ABSTRACT: The EinsteinDirac equation is considered in the RobertsonWalker spacetime. Solutions of the equation are looked for in the class of standard solutions of the Dirac equation. It is shown that the EinsteinDirac equation does not have standard solutions for both massive and massless Dirac field. Also superpositions of massive standard solutions are not solutions of the EinsteinDirac equation. The result, that is briefly commented, is coherent and complementary to other existing results.International Journal of Theoretical Physics 08/2009; 48(8):23052310. DOI:10.1007/s1077300900199 · 1.19 Impact Factor 
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ABSTRACT: The study of the field equation of arbitrary spin in RobertsonWalker spacetime, previously separated by variable separation, is completed. The integration of the separated radial equations is performed in an unified 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 functions such as the hypergeometric, the polynomial, the polynomiallike 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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