Spin connection as Lorentz gauge field: propagating torsion

Abstract

We propose a modified gravitational action containing besides the Einstein-Cartan term some quadratic contributions resembling the Yang-Mills lagrangian for the Lorentz spin connections. We outline how a propagating torsion arises and we solve explicitly the linearised equations of motion on a Minkowski background. We identify among torsion components six degrees of freedom: one is carried by a pseudo-scalar particle, five by a tachyon field. By adding spinor fields and neglecting backreaction on the geometry, we point out how only the pseudo-scalar particle couples directly with fermions, but the resulting coupling constant is suppressed by the ratio between fermion and Planck masses. Including backreaction, we demonstrate how the tachyon field provides causality violation in the matter sector, via an interaction mediated by gravitational waves.

7 pages, no figures, new section added

References in corpus (5)

• Big-Bang Nucleosynthesis
• New Physics Contributions to the Muon Anomalous Magnetic Moment: A Numerical Code
• A discussion on the most general torsion-gravity with electrodynamics for Dirac spinor matter fields
• Fundamentals and recent developments in non-perturbative canonical Quantum Gravity
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Cited by in corpus (3)

• A first-order approach to conformal gravity
• Pure gauge theory for the gravitational spin connection
• From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras