A Note on Parity Violation and the Immirzi Parameter

Abstract

There has been considerable recent interest in the Immirzi parameter as a measure of parity violating effects in the classical theory of gravitation with fermion coupling. Most recently it was shown that the Immirzi parameter together with the non-minimal coupling constant of Dirac spinors provides the measure for parity violating spin-spin interaction terms in the effective field theory. For complex values of the Immirzi parameter, the resulting effective field theory yields complex values for the torsion, and a non-unitary effective field theory that blows up for the special cases $\gamma =\pm i$ where the gravitational kinetic term is the Ashtekar action. We show that by restricting ourselves to real values for the torsion, there is a natural set of choice for the non-minimal coupling constant that yields real and unitary effective field theory that does not blow up for the special cases $\gamma =\pm i$. We then show that these particular values for the non-minimal coupling coefficients most naturally follow from a non-minimal pseudo-kinetic term in the fermion Lagrangian.

7 pages

References in corpus (2)

• Quantum Gravity, Torsion, Parity Violation and all that
• Physical effects of the Immirzi parameter

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