Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions

TL;DR

This paper explores how the deformation of symmetries on the Groenewold-Moyal plane alters quantum statistics, leading to Pauli-forbidden energy levels and transitions with potential implications for the quantum Hall effect.

Contribution

It demonstrates that the deformed symmetry actions on the Groenewold-Moyal plane modify Bose and Fermi relations, resulting in novel physical phenomena like forbidden energy levels.

Findings

Deformation of symmetry actions alters quantum statistics.

Pauli-forbidden energy levels and transitions occur.

Potential applications to the quantum Hall effect.

Abstract

The Groenewold-Moyal plane is the algebra A_\theta(R^(d+1)) of functions on R^(d+1) with the star-product as the multiplication law, and the commutator [x_\mu,x_\nu] =i \theta_{\mu \nu} between the coordinate functions. Chaichian et al. and Aschieri et al. have proved that the Poincare group acts as automorphisms on A_\theta(R^(d+1))$ if the coproduct is deformed. (See also the prior work of Majid, Oeckl and Grosse et al). In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Aschieri et al. In this paper we show that for this new action, the Bose and Fermi commutation relations are deformed as well. Their potential applications to the quantum Hall effect are pointed out. Very striking consequences of these deformations are the occurrence of Pauli-forbidden energy levels and transitions. Such new effects are discussed in simple cases.