Sachindeo Vaidya

SPIN AND STATISTICS ON THE GROENEWOLD–MOYAL PLANE: PAULI-FORBIDDEN LEVELS AND TRANSITIONS

The Groenewold–Moyal plane is the algebra

Statistics and UV-IR mixing with twisted Poincaré invariance

{\mathcal A}_\theta({\mathbb R}^{d+1})

Twisted conformal symmetry in noncommutative two dimensional quantum field theory

of functions on ℝd+1 with the *-product as the multiplication law, and the commutator

S matrix on the Moyal plane: Locality versus Lorentz invariance

[\hat{x}_\mu,\hat{x}_\nu] =i\theta_{\mu \nu}\, (\mu,\nu=0,1,\ldots,d)

Spontaneous Lorentz violation: the case of infrared QED

between the coordinate functions. Chaichian et al.1 and Aschieri et al.2 have proved that the Poincare group acts as automorphisms on

Nonextremality, chemical potential, and the infrared limit of large N thermal QCD

{\mathcal A}_\theta({\mathbb R}^{d+1})

QED ON THE GROENEWOLD–MOYAL PLANE

if the coproduct is deformed. (See also the prior work of Majid,3 Oeckl4 and Grosse et al.5) In fact, the diffeomorphism group with a deformed coproduct also does so according to the results of Ref. 2. 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.

Quantum entropic ambiguities: Ethylene

We elaborate on the role of quantum statistics in twisted Poincare invariant theories. It is shown that, in order to have twisted Poincare group as the symmetry of a quantum theory, statistics must be twisted. It is also confirmed that the removal of UV-IR mixing (in the absence of gauge fields) in such theories is a natural consequence.

Thermal correlation functions of twisted quantum fields

By twisting the commutation relations between creation and annihilation operators, we show that quantum conformal invariance can be implemented in the 2-d Moyal plane. This is an explicit realization of an infinite dimensional symmetry as a quantum algebra.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

Twisted quantum field theories on the Groenewold-Moyal plane are known to be nonlocal. Despite this nonlocality, it is possible to define a generalized notion of causality. We show that interacting quantum field theories that involve only couplings between matter fields, or between matter fields and minimally coupled U(1) gauge fields are causal in this sense. On the other hand, interactions between matter fields and non-Abelian gauge fields violate this generalized causality. We derive the modified Feynman rules emergent from these features. They imply that interactions of matter with non-Abelian gauge fields are not Lorentz- and CPT-invariant.