The Origin of Chiral Anomaly and the Noncommutative Geometry

TL;DR

This paper explores the origin of chiral anomaly within noncommutative geometry by quantizing a gauge-extended spinor model on a noncommutative sphere, revealing finite modes and a non-perturbative UV-regular structure.

Contribution

It introduces a noncommutative version of the Schwinger model on a sphere, providing an exact expression for the chiral anomaly and demonstrating UV-regularity and finite dynamical modes.

Findings

Exact expression for the chiral anomaly on a noncommutative sphere

Finite number of dynamical modes in the noncommutative model

Model reduces to standard formula in the commutative limit

Abstract

We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra ${\cal A}={\cal U}{u(2))}$. The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version of the model contains only a finite number of dynamical modes and is non-perturbatively UV-regular. An exact expresion for the chiral anomaly is found. In the commutative limit the standard formula is recovered.