Theories on noncommutative spaces and deformed symmetries

TL;DR

This thesis explores noncommutative spaces in quantum mechanics, field theory, and gravity, focusing on how symmetries are deformed in these contexts and analyzing their underlying structures.

Contribution

It provides a detailed analysis of symmetry deformations in noncommutative theories across multiple physical frameworks.

Findings

Deformation of spacetime symmetries in noncommutative quantum mechanics

Altered gauge symmetries in noncommutative field theories

Insights into symmetry structures in noncommutative gravity

Abstract

In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external space time symmetries and the internal gauge symmetry in noncommutative theories are analyzed in detail.