Noncommutative Quantum Field and Gauge Theories

This monograph endeavours to give an overview of the rapidly developing noncommutative quantum field and gauge theories. The effects of nonlocality and violation of Lorentz invariance, two intrinsic features of noncommutative field theories, are explored in relation to fundamental issues in physics, like the unitarity, causality, CPT and spin-statistics theorems, as well as in gauge field theory and models for particle interactions, such as the Standard Model. Phenomenological implications of noncommutative gauge theories are also discussed. Achievements in constructing an axiomatic formulation of noncommutative quantum field theories are presented. The recently found symmetry, namely the twisted Poincaré – as the analogue of relativity for the noncommutative space-time – is particularly emphasized in its various manifestations, including a possible gauge theory of gravity. The book is intended for graduate students and researchers interested in noncommutative geometry and quantum field and gauge theories.