Article

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

Department of Physics, University of Milan, Milano, Lombardy, Italy

International Journal of Theoretical Physics (Impact Factor: 1.18). 03/1998; 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 spinor formulation of the massive spin-1 equation is considered in the general Robertson-Walker space-time. 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/i2005-10058-7 - [Show abstract] [Hide abstract]

**ABSTRACT:**Exact solutions of the Dirac equation in the Robertson–Walker space-time are obtained by an elementary separation method that represents a straightforward improvement of previous results. The radial equations are integrated by reporting them to hypergeometric equations. The separated time equations are solved exactly for three models of universe expansion and integrated by series in a case of the standard cosmological model. The integration of both radial and time equations represents an improvement of previous results.International Journal of Theoretical Physics 12/2005; 45(1):44-52. DOI:10.1007/s10773-005-9007-x · 1.18 Impact Factor -
##### Article: The Einstein-Dirac Equation in Robertson-Walker Space-Time Does Not Admit Standard Solutions

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**ABSTRACT:**The Einstein-Dirac equation is considered in the Robertson-Walker space-time. Solutions of the equation are looked for in the class of standard solutions of the Dirac equation. It is shown that the Einstein-Dirac equation does not have standard solutions for both massive and massless Dirac field. Also superpositions of massive standard solutions are not solutions of the Einstein-Dirac equation. The result, that is briefly commented, is coherent and complementary to other existing results.International Journal of Theoretical Physics 08/2009; 48(8):2305-2310. DOI:10.1007/s10773-009-0019-9 · 1.18 Impact Factor

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