From Poincare to affine invariance: How does the Dirac equation generalize?
General Relativity and Quantum Cosmology
2009-11-07 v2 High Energy Physics - Theory
Abstract
A generalization of the Dirac equation to the case of affine symmetry, with SL(4,R) replacing SO(1,3), is considered. A detailed analysis of a Dirac-type Poincare-covariant equation for any spin j is carried out, and the related general interlocking scheme fulfilling all physical requirements is established. Embedding of the corresponding Lorentz fields into infinite-component SL(4,R) fermionic fields, the constraints on the SL(4,R) vector-operator generalizing Dirac's gamma matrices, as well as the minimal coupling to (Metric-)Affine gravity are studied. Finally, a symmetry breaking scenario for SA(4,R) is presented which preserves the Poincare symmetry.
Keywords
Cite
@article{arxiv.gr-qc/0111088,
title = {From Poincare to affine invariance: How does the Dirac equation generalize?},
author = {Ingo Kirsch and Djordje Sijacki},
journal= {arXiv preprint arXiv:gr-qc/0111088},
year = {2009}
}
Comments
34 pages, LaTeX2e, 8 figures, revised introduction, typos corrected