Dirac Particles in Coulomb Like Field in FLRW–Space

Abstract

Behaviour of the Dirac particle in Coulomb like field in FLRW space is investigated. Firstly, the Maxwell equations, in terms of the vector potentials are solved to identify the Lorentz and Coulomb like gauges. The radial Coulomb like potential is solved in terms of Legendre functions. Then the Dirac equation is generalized to include this potential and the angular part is separated and solved. The radial and temporal parts of the massless case is also separated and solved. But the massive case remains coupled. This is still reduced to the case where the Dirac particle can be represented as being in a combined gravitational and electric potential. This effective potential is found to develop an attractive well, which may require a revisit to the recombination era.