Braided Field Quantization from Quantum Poincare Covariance

TL;DR

This paper shows that quantum-deformed Poincare symmetries lead to a braided algebra of fields and braided locality in noncommutative quantum field theory, emphasizing the necessity of a fully braided formalism.

Contribution

It introduces the concept of braided algebra and locality in quantum-deformed NC QFT, extending the framework to include braiding throughout the formalism.

Findings

Braided algebra of fields arises from quantum Poincare covariance.

Braided locality is implied by the braided commutator of fields.

Demonstrated with NC scalar free fields on Moyal-Weyl space.

Abstract

We demonstrate that the covariance of the algebra of quantum NC fields under quantum-deformed Poincare symmetries implies the appearence of braided algebra of fields and the notion of braided locality in NC QFT. We briefly recall the historical development of NC QFT which was firstly formulated in the framework using classical relativistic symmetries but further it was described as generated by the quantum-deformed symmetries. We argue that consistent covariant quantum-deformed formalism requires "braiding all the way", in particular braided commutator of deformed field oscillators as well as the braid between the field oscillators and noncommutative Fourier exponentials. As example of braided quantum-deformed NC QFT we describe the NC scalar free fields on noncommutative canonical (Moyal-Weyl) space-time with braided c-number field commutator which implies braided locality.