Braided tensor products and the covariance of quantum noncommutative free fields

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 of functions on noncommutative spacetime, the product in the algebra of deformed field oscillators, and the braiding by factor between algebras and . For noncommutativity of quantum spacetime generated by the twist factor, we shall employ the ⋆-product realizations of the algebra in terms of functions on the 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 a Poincare group manifold. We shall calculate the braided field commutator covariant under deformed Poincare symmetries, which for free quantum noncommutative fields provides the field quantization condition and is given by the standard Pauli–Jordan function. For the illustration of our new scheme, we present explicit calculations for the well-known case in the literature of canonically deformed free quantum fields.