Fuzzy Physics

TL;DR

This paper discusses the fuzzification of coadjoint orbits and their quantum field theories, highlighting how non-commutative matrix models serve as effective regularizations that preserve symmetries and topological features.

Contribution

It introduces a method for fuzzifying coadjoint orbits and their QFTs, advancing the use of fuzzy manifolds in regularizing quantum field theories.

Findings

Preserves symmetries and topological features

Overcomes fermion-doubling problem

Effective discretization of spacetime

Abstract

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem . In this thesis, the fuzzification of coadjoint orbits and their QFT's are put forward.