Spin-base invariance of Fermions in arbitrary dimensions

Abstract

The concept of spin-base invariance is extended to arbitrary integer dimension $d\ge 2$. 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.

26 pages

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Cited by in corpus (4)

• Quantum gravity and Standard-Model-like fermions
• Ising and Gross-Neveu model in next-to-leading order
• Asymptotically Safe Gravity with Fermions
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds