Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields

TL;DR

This paper introduces a framework for free quantum noncommutative fields using braided tensor products, analyzing their covariance under deformed symmetries and providing explicit calculations for canonical deformations.

Contribution

It develops a new algebraic approach to noncommutative quantum fields with braided tensor products and explores their covariance properties under deformed Poincare symmetries.

Findings

Covariant braided field commutator matches standard Pauli-Jordan function.

Framework applies to canonical noncommutative deformations.

Provides explicit calculations for free quantum fields in noncommutative space.

Abstract

We introduce the free quantum noncommutative fields as described by braided tensor products. The multiplication of such fields is decomposed into three operations, describing the multiplication in the algebra M of functions on noncommutative space-time, the product in the algebra H of deformed field oscillators, and the braiding by factor Psi_{M,H} between algebras M and H. For noncommutativity generated by the twist factor we shall employ the star-product realizations of the algebra M in terms of functions on standard Minkowski space. The covariance of single noncommutative quantum fields under deformed Poincare symmetries is described by the algebraic covariance conditions which are equivalent to the deformation of generalized Heisenberg equations on Poincare group manifold. We shall calculate the covariant braided field commutator, which for free quantum noncommutative fields provides the field quantization condition and is given by standard Pauli-Jordan function. For ilustration of our new scheme we present explicit calculations for the well-known case in the literature of canonically deformed free quantum fields.