Canonical conjugated Dirac equation in a curved space

Details Canonical conjugated Dirac equation in a curved space Canonical conjugated Dirac equation in a curved space

2012-02-23

arxiv.org/abs/1202.5100v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

mention of Lagrangian is omitted

Scientific paper

It is shown that the calculation of Dirac operator for the spherical coordinate system with spherical Dirac matrices and using the spin connection formalism is in the contradiction with the definition of standard Dirac operator in the spherical Minkowski coordinate system. It is shown that such contradiction one can avoid by introducing a canonical conjugated covariant derivative for the spinor field. The Dirac equation solution on the Reissner - Nordstr\"om background is obtained. The solution describes a bound state of a charged particle.

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