English

$\bar{SL}(4,R)$ Embedding for a 3D World Spinor Equation

General Relativity and Quantum Cosmology 2009-11-10 v1

Abstract

A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the SLˉ(n,R)\bar{SL}(n,R) group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding SLˉ(3,R)\bar{SL}(3,R) vector operator XμX_{\mu}, that plays a role of Dirac's γμ\gamma_{\mu} matrices, into SLˉ(4,R)\bar{SL}(4,R). Decomposition of the unitary irreducible spinorial SLˉ(4,R)\bar{SL}(4,R) representations gives rise to an explicit form of the infinite XμX_{\mu} matrices.

Keywords

Cite

@article{arxiv.gr-qc/0409080,
  title  = {$\bar{SL}(4,R)$ Embedding for a 3D World Spinor Equation},
  author = {Djordje Sijacki},
  journal= {arXiv preprint arXiv:gr-qc/0409080},
  year   = {2009}
}
R2 v1 2026-07-22T12:41:04.050Z