From Poincare to affine invariance: How does the Dirac equation generalize?

Details From Poincare to affine invariance: How does the Dirac equation generalize? From Poincare to affine invariance: How does the Dirac equation generalize?

2001-11-26

arxiv.org/abs/gr-qc/0111088v2

Class.Quant.Grav. 19 (2002) 3157-3178

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, LaTeX2e, 8 figures, revised introduction, typos corrected

Scientific paper

10.1088/0264-9381/19/12/305

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.

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