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

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

2004-09-21

arxiv.org/abs/gr-qc/0409080v1

Class.Quant.Grav. 21 (2004) 4575

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1088/0264-9381/21/19/007

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

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