Proceedings of the International Conference on Geometry, Integrability and Quantization

Search for the Geometrodynamical Gauge Group: Hypotheses and Some Results

Abstract

Discussed is the problem of the mutual interaction between spinor and gravitational fields. The special stress is laid on the problem of the proper choice of the gauge group responsible for the spinorial geometrodynamics. According to some standard views this is to be the local, i.e., $x$-dependent, group SL$(2,\mathbb{C})$, the covering group of the Lorentz group which rules the internal degrees of freedom of gravitational cotetrad. Our idea is that this group should be replaced by SU$(2,2)$, i.e., the covering group of the Lorentz group in four dimensions. This leads to the idea of Klein-Gordon-Dirac equation which in a slightly different context was discovered by Barut and coworkers. The idea seems to explain the strange phenomenon of appearing leptons and quarks in characteristic, mysterious doublets in the electroweak interaction.

Article information

Dates
First available in Project Euclid: 13 July 2015

https://projecteuclid.org/ euclid.pgiq/1436793141

Digital Object Identifier
doi:10.7546/giq-9-2008-66-132

Mathematical Reviews number (MathSciNet)
MR2436266

Zentralblatt MATH identifier
1205.83052

Citation

Sławianowski, Jan J.; Kovalchuk, Vasyl. Search for the Geometrodynamical Gauge Group: Hypotheses and Some Results. Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, 66--132, Softex, Sofia, Bulgaria, 2008. doi:10.7546/giq-9-2008-66-132. https://projecteuclid.org/euclid.pgiq/1436793141