A Rotating Field Solution of the Dirac Equation
Didimos K. V *
Department of Mathematics, Sacred Heart College, Thevara, Kochi-682013, India.
R.S. Chakravarti
Department of Mathematics, Cochin University of Science and Technology, Kochi-682022, India.
Tonny K. B
Department of Mathematics, College of Engineering Trivandrum, Kerala 695016, India.
*Author to whom correspondence should be addressed.
Abstract
A deterministic field theory of the Dirac equation along lines that Einstein, and possibly Dirac, may have approved of, was given by Toyoki Koga. In this paper, we work out some relevant properties of Koga’s solution to the Dirac equation. In particular, we consider his claim that the solution contains a term representing a rotating field. We confirm his claim and find additional information on coordinate transformations using the Hopf map. We also establish that the rotating field of the solution to the Dirac equation given in this paper is compatible with Pauli spin theory.
Keywords: Dirac equation, klein-gordon equation, rotating field