Factoring the Dispersion Relation in the Presence of Lorentz Violation

Details Factoring the Dispersion Relation in the Presence of Lorentz Violation Factoring the Dispersion Relation in the Presence of Lorentz Violation

2010-01-21

arxiv.org/abs/1001.3839v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages

Scientific paper

We produce an explicit formula for the dispersion relation for the Dirac Equation in the Standard Model Extension (SME) in the presence of Lorentz violation. Our expression is obtained using a novel techniques which exploit the algebra of quaternions. The dispersion relation is found to conveniently factor in two special cases that each involve a mutually exclusive set of non-vanishing Lorentz-violating parameters. This suggests that a useful approach to studies of Lorentz-violating models is to split the parameter space into two separate pieces, each of which yields a simple, tractable dispersion relation that can be used for analysis.

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