Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections
High Energy Physics - Theory
2015-10-22 v4 General Relativity and Quantum Cosmology
Quantum Physics
Abstract
By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also require that squaring the equation give the Klein-Gordon equation in a curved space in its canonical from (without spinor components coupling and with no first order derivatives). These requirements result in matrix operator algebra for the Dirac gamma matrices that involves a universal curvature constant. We obtain exact solutions of the Dirac and Klein-Gordon equations in 1+1 space-time for a given static metric.
Keywords
Cite
@article{arxiv.1106.2236,
title = {Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections},
author = {A. D. Alhaidari and A. Jellal},
journal= {arXiv preprint arXiv:1106.2236},
year = {2015}
}
Comments
In this version, Eq. (17) and Eqs. (18a-18c) are Corrected