Global surpluses of spin-base invariant fermions

TL;DR

This paper advocates for the inclusion of local spin-base invariance in quantum gravity theories, demonstrating its conceptual and practical benefits through explicit constructions in curved space.

Contribution

It introduces the advantages of spin-base invariant formalism for Dirac fermions in curved space and constructs a global Clifford algebra on a 2-sphere, highlighting its novelty.

Findings

Supports local spin-base invariance as a property of quantum gravity

Constructs a global Clifford algebra on a 2-sphere in this formalism

Shows limitations of non-invariant vielbein formalism

Abstract

The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin-base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism.