Volume elements and torsion

Abstract

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, $T_{\mu }={\partial }_{\mu }\theta$, and that the modified volume element ${\tau }_{\theta }=e^{\theta }\sqrt{g}d{x}^1\wedge ...\wedge d{x}^n$ be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects.

Revtex, 8 pages, 1 figure. v2 includes a discussion on $\lambda$-symmetry

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Cited by in corpus (10)

• Minimal coupling in presence of non-metricity and torsion
• Transition to Zero Cosmological Constant and Phantom Dark Energy as Solutions Involving Change of Orientation of Space-Time Manifold
• Massless DKP field in Lyra manifold
• Einstein-Cartan gravity with Holst term and fermions
• Local electromagnetic duality and gauge invariance
• Nonuniqueness of gravity-induced fermion interaction in the Einstein-Cartan theory
• Propagating torsion in the Einstein frame
• On the choice of coupling procedure for the Poincaré gauge theory of gravity
• Modified coupling procedure for the Poincaré gauge theory of gravity
• Maxwell field with Torsion