Spin-base invariance of Fermions in arbitrary dimensions

TL;DR

This paper extends the concept of spin-base invariance to arbitrary dimensions, providing explicit formulas and revealing hidden symmetries in the vielbein formalism, which simplifies calculations in fermionic theories.

Contribution

It introduces a generalization of spin-base invariance to any dimension and uncovers hidden symmetries, along with explicit formulas for the spin connection.

Findings

Explicit formulas for spin connection in arbitrary dimensions

Discovered hidden spin-base invariance in vielbein formalism

Constructed a simple Lorentz symmetric gauge for Dirac matrices

Abstract

The concept of spin-base invariance is extended to arbitrary integer dimension $d \geq 2$. Explicit formulas for the spin connection as a function of the Dirac matrices are found. We disclose the hidden spin-base invariance of the vielbein formalism and give a detailed motivation for this symmetry from first principles. The common Lorentz symmetric gauge for the vielbein is constructed for the Dirac matrices, even for metrics which are not linearly connected. Under certain criteria, it constitutes the simplest possible gauge, demonstrating why this gauge is so useful.