Some Aspects of Quantum Mechanics and Quantum Field Theory on Quantum Space- Time

TL;DR

This thesis explores quantum mechanics and quantum field theory on non-commutative space-time using toy models to understand symmetry properties and fundamental aspects in a simplified setting.

Contribution

It provides insights into symmetries and quantum phenomena on non-commutative space-time through simplified (0+1) dimensional models.

Findings

Symmetries are partially preserved in non-commutative quantum models.

Toy models reveal key features of quantum mechanics on non-commutative space-time.

Insights may inform broader understanding of quantum field theories in non-commutative geometries.

Abstract

This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in (0 + 1) dimension. This allows one to gain some insights into this and other related issues in a more transparent manner.