Search for fundamental models with affine symmetry: some results, some hypotheses and some essay. (English) Zbl 1080.83004

Sławianowski, Jan Jerzy

Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 126-172 (2005).

The author studies the tetrad formalism in gravity with certain modifications. The absolute framework of the field-theoretic model consists of a differential “space-time” manifold \(M\) and linear space \(V\), both of the same real dimension \(n\). The main novelty of the presented model is that it is the total globally acting GL\((n,R)\) that is used as the group of internal symmetry. The interaction with the bispinor field is discussed. This model may also have to do with the problem of dark matter. The presented model can be also interpreted as something between field theory and continuum mechanics, as a kind of cosmic ether concept revisited.
For the entire collection see [Zbl 1066.53003].

Reviewer: Vladimir Dzhunushaliev (Bishkek)

MSC:

83C05	Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C60	Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83D05	Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

Keywords:

tetrads; affine symmetry