Separation of variables in the Dirac equation for one class of non-diagonal metrics

Cabos, William D.; Shishkin, G.V.

doi:10.1088/0264-9381/9/3/012

Cited by 2 publications

(1 citation statement)

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“…The point-dependent similarity transformation S [3] is usually called a "local" similarity transformation (e.g. [4]). It should not alter the physical properties of the fermions described by the modified Dirac equation, and is thus a local gauge transformation.…”

Section: Introductionmentioning

confidence: 99%

A Simpler Solution of the Non-Uniqueness Problem of the Covariant Dirac Theory

Arminjon

2013

Int. J. Geom. Methods Mod. Phys.

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Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved, by restricting the choice of thé Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isbtropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

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Section: Introductionmentioning

confidence: 99%