Dirac and Klein-Gordon Equations in Curved Space

Source: arXiv

ABSTRACT We introduce matrix operator algebra involving a universal curvature
constant. Using elements of the algebra, we write the Dirac equation without
the need for spin connections or vierbeins. Iterating the equation and using
the algebra leads to the Klein-Gordon equation in curved space in its canonical
from (without first order derivatives). We obtain exact solutions of the Dirac
and Klein-Gordon equations for a static diagonal metric.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The present reading is part of our on-going attempt at the foremost endeavour of physics since man began to comprehend the heavens and the earth. We present a much more improved unified field theory of all the forces of Nature i.e. the gravitational, the electromagnetic, the weak and the strong nuclear forces. The proposed theory is a radical improvement of Professor Hermann Weyl [1– 3]'s supposed failed attempt at a unified theory of gravitation and electromagnetism. As is the case with Professor Weyl's theory, unit vectors in the resulting/proposed theory vary from one point to the next, albeit, in a manner such that they are compelled to yield tensorial affinities. In a separate reading [4], the Dirac equation is shown to emerge as part of the description of the these variable unit vectors. The nuclear force fields – i.e., electromagnetic, weak and the strong – together with the gravitational force field are seen to be described by a four vector field Aµ, which forms part of the body of the variable unit vectors and hence the metric of spacetime. The resulting theory very strongly appears to be a logically consistent and coherent unification of classical and quantum physics and at the same time a grand unity of all the forces of Nature. Unlike most unification theories, the present proposal is unique in that it achieves unification on a four dimensional continuum of spacetime without the need for extra-dimensions.Imagination will often carry us to worlds that never were. But without it, we go nowhere[5]." – Carl Edward Sagan (1934 − 1996) INTRODUCTION
    Journal of Modern Physics 07/2014; 5(16):1733-1766. DOI:10.4236/jmp.2014.516173

Full-text (2 Sources)

Available from
Jun 5, 2014