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arXiv · 1106.2236

Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections

A. D. Alhaidari·A. Jellal
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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.

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A. D. Alhaidari, A. Jellal. 2015-07-11. Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections. https://doi.org/10.1016/j.physleta.2015.08.021

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