Noncommutative Quantum Field Theory: A Confrontation of Symmetries
M. Chaichian, K. Nishijima, T. Salminen, A. Tureanu
TL;DR
This paper examines the structure of noncommutative quantum field theories, focusing on their symmetries, causality, and dynamical properties, and challenges the notion that they are equivalent to traditional QFTs.
Contribution
It introduces a formulation of noncommutative fields based on twisted Poincaré symmetry and refutes the claim of their equivalence to commutative quantum field theories.
Findings
Supports the light-wedge causality condition
Provides integrability conditions for the Tomonaga-Schwinger equation
Refutes the identity between commutative and noncommutative QFTs with twisted symmetry
Abstract
The concept of a noncommutative field is formulated based on the interplay between twisted Poincar\'e symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting this construction, such as the light-wedge causality condition and the integrability condition for Tomonaga-Schwinger equation, are presented. Based on this analysis, the claim of the identity between commutative QFT and noncommutative QFT with twisted Poincar\'e symmetry is refuted.
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