$\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory

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 $\kappa$-Poincaré group. This necessitates a braided tensor product. We study the representations of this product, and prove that $\kappa$-Poincaré-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 $\kappa$-Poincaré-invariant quantum field theory, and identify some open problems.

27 pages, 3 figures

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• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Light Propagation in $\kappa$-Minkowski Space-Time: Gauge Ambiguities and Invariance
• T-Minkowski noncommutative spacetimes II: classical field theory
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Quantum Groups and Polymer Quantum Mechanics
• Doubly Quantum Mechanics
• Formal developments in curved momentum space: the quantum field theory roadmap