We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective lagrangian which turns out to involve two parameters, one measuring the non-minimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of non-minimal coupling the effective lagrangian contains an axial-vector interaction leading to parity violation. Alternatively, in the case of minimal coupling there is no parity violation and the effective lagrangian contains only the usual axial-axial interaction. In this situation the real values of the Immirzi parameter are not at all constrained. On the other hand, purely imaginary values of the Immirzi parameter lead to violations of unitarity for the case of non-minimal coupling. Finally, the effective lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.

A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which

This is a set of LATEX’ed notes from Cornell University’s Physics 7661 (special topics in theoretical high energy physics) course by Yuval Grossman in Fall 2010. The lectures as given were flawless, all errors contained herein reflect solely the typist’s editorial and/or intellectual deficiencies! Contents

Detection of parity-violating weak interactions in the 1s 1- 2p 1 z z two photon transitions in hydrogen is discussed. Polarization rota-tion of one of the two photon beams exciting the transition is computed for general theories of the weak interaction and in particular for the SU2 x Ul theory due to Weinberg and Salam. (Submitted to Phys. Rev. A.) *Work supported by the Energy Research and Development Administration.

Tunable single frequency Nd:GdVO4 laser and its spectroscopic applications