Gravitational interaction of hadrons: Band-spinor representations of GL(n,R)

1 October 1977

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 74 (10) , 4157-4159
https://doi.org/10.1073/pnas.74.10.4157

Abstract

We demonstrate the existence of double-valued linear (infinite) spinorial representations of the group of general coordinate transformations. We discuss the topology of the group of general coordinate transformations and its subgroups GA(nR), GL(n,R), SL(nr) for n = 2,3,4, and the existence of a double covering. We present the construction of band-spinor representations of GL(n,R) in terms of Harish-Chandra modules.It is suggested that hadrons interact with gravitation as band-spinors of that type. In the metric-affine extension of general relativity, the hadron intrinsic hypermomentum is minimally coupled to the connection, in addition to the coupling of the energy momentum tensor to the vierbeins. The relativistic conservation of intrinsic hypermomentum fits the observed regularities of hadrons: SU(6) ( approximately spin independence), scaling, and complex-J trajectories. The latter correspond to volume-preserving deformations (confinement?) exciting rotational bands.

Keywords

This publication has 1 reference indexed in Scilit:

Group Theoretical Discussion of Relativistic Wave Equations
Proceedings of the National Academy of Sciences, 1948