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A Note on Parity Violation and the Immirzi Parameter

Andrew Randono
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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 $γ=\pm i$ 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 $γ=\pm i$. 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.

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Andrew Randono. 2005-09-30. A Note on Parity Violation and the Immirzi Parameter. https://arxiv.org/abs/hep-th/0510001

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