$\kappa$-Poincar\'e-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory

TL;DR

This paper explores the construction of multiparticle quantum field theories on a specific noncommutative spacetime, showing that certain invariant functions remain commutative and identical to classical counterparts, thus enabling a consistent theory.

Contribution

It introduces a braided tensor product framework for $ ext{kappa}$-Poincaré-invariant quantum fields, demonstrating the commutativity of N-point functions and outlining a path to a free scalar quantum field theory.

Findings

$ ext{kappa}$-Poincaré-invariant N-point functions are commutative.

2-point functions are identical to classical undeformed functions.

Construction of a free scalar $ ext{kappa}$-Poincaré-invariant quantum field theory is outlined.

Abstract

We discuss the obstruction to the construction of a multiparticle field theory on a $\kappa$-Minkowski noncommutative spacetime: the existence of multilocal functions which respect the deformed symmetries of the problem. This construction is only possible for a light-like version of the commutation relations, if one requires invariance of the tensor product algebra under the coaction of the $\kappa$-Poincar\'e group. This necessitates a braided tensor product. We study the representations of this product, and prove that $\kappa$-Poincar\'e-invariant N-point functions belong to an Abelian subalgebra, and are therefore commutative. We use this construction to define the 2-point Whightman and Pauli--Jordan functions, which turn out to be identical to the undeformed ones. We finally outline how to construct a free scalar $\kappa$-Poincar\'e-invariant quantum field theory, and identify some open problems.