Spin-Statistics Correlations in Various Noncommutative Field Theories

TL;DR

This thesis explores noncommutative field theories on the Groenewold-Moyal plane, demonstrating their renormalizability, analyzing twisted statistics, and proposing potential experimental signatures in cosmic ray correlations.

Contribution

It introduces a comprehensive study of renormalization, twisted internal symmetries, and phenomenological implications of noncommutative field theories on the GM plane.

Findings

Noncommutative theories with polynomial matter interactions are renormalizable if their commutative counterparts are.

All such theories share the same fixed points and beta functions as the commutative theories.

Twisted statistics modify correlation functions, enabling potential experimental detection via HBT correlations in cosmic rays.

Abstract

In this thesis we study field theories written on a particular model of noncommutative spacetime, the Groenewold-Moyal (GM) plane. We start with briefly reviewing the novel features of field theories on GM plane e.g. the $\ast$-product, restoration of Poincar\'e-Hopf symmetry and twisted commutation relations. We then discuss our work on renormalization of field theories on GM plane. We show that any generic noncommutative theory involving pure matter fields with polynomial interactions, is a renormalizable theory if the analogous commutative theory is renormalizable. We further show that all such noncommutative theories will have same fixed points and $\beta$-functions for the couplings, as that of the analogous commutative theory. The unique feature of these field theories is the twisted statistics obeyed by the particles. Motivated by it, we look at the possibility of twisted statistics by deforming internal symmetries instead of spacetime symmetries. We construct two different twisted theories which can be viewed as internal symmetry analogue of the GM plane and dipole field theories which arise in the low energy limit of certain string configurations. We further study their various properties like the issue of causality and the scattering formalism. Having studied the mathematical properties of noncommutative and twisted internal symmetries we move on to discuss their potential phenomenological signatures. We first discuss the noncommutative thermal correlation functions and show that because of the twisted statistics, all correlation functions except two-point function get modified. Finally we discuss the modifications in Hanbury-Brown Twiss (HBT) correlation functions due to twisted statistics on GM plane and the potential of observing signatures of noncommutativity by doing a HBT correlation experiment with Ultra High Energy Cosmic Rays (UHECRs).