Article

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

International Journal of Theoretical Physics (Impact Factor: 1.09). 01/1998; 37(3):995-1009. DOI: 10.1023/A:1026693218876

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**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. · 1.09 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 01/2009; 48(8):2305-2310. · 1.09 Impact Factor - [Show abstract] [Hide abstract]

**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.Adv. Studies Theor. Phys. 01/2010; 4203030(02).

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