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

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(nR) SL4nr) for n = 2,3,4, and the existence of a double covering. We present the construction of band-spinor representations of GLtnR) 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) (-spin independence), scaling, and complex-J trajectories. The latter correspond to volumepreserving deformations (confinement?) exciting rotational ands.

Hyperfluid — a model of classical matter with hypermomentum

“…It is interesting to obtain the exact non-vacuum solutions for the gravitational field equations in astrophysical and cosmological (very early stages) setting, this work is now in progress. Further development of the hyperfluid model should give an answer to an important question: is it possible to recover this medium in a semiclassical treatment of the quantum matter with hypermomentum -such as, for example, the manifields [26][27][28]?…”

On the chiral anomaly in non-Riemannian spacetimes

“…In this framework, the linear groups SL(3, R) [1] and SL(4, R) [2] play decisive roles for the representation of matter fields. Very early, L. Biedenharn and his collaborators [3] or students [4] investigated the half-integer representations (of the covering group) of the SL(3, R).…”

World spinors—Construction and some applications

“…'s results, published in 1975 [9], were extensive and "final", as emphasized several years later in a more mathematically oriented study [10]. Thus, when in 1977, YN demonstrated [11,12,13] the relevance of these results to an issue in Gravity, namely the erroneous rulingout of curved space spinors (world spinors), it was natural that the two authors should converge in their interests -and the present collaboration was born.…”

“…Almost every textbook in general relativity theory, upon reaching the subject of spinors, contains a sentence such as "... there are no representations of GL(4, R), or even 'representations up to a sign', which behave like spinors under the Lorentz subgroup". Though the correct answer has been known since 1977 [11,12,13], the same type of statement continues to appear in more recent texts. The present authors were much encouraged in their dealing with the issue of spinors in a curved space by the convergence of their interests in this matter with the investigation of Metric-Affine manifolds initiated by F.W.…”