Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT

Abstract

In this study, we construct a 1+1-dimensional, relativistic, free, complex scalar Quantum Field Theory on the noncommutative spacetime known as lightlike $\kappa$-Minkowski. The associated $\kappa$-Poincaré quantum group of isometries is triangular, and its quantum R matrix enables the definition of a braided algebra of N points that retains $\kappa$-Poincaré invariance. Leveraging our recent findings, we can now represent the generators of the deformed oscillator algebra as nonlinear redefinitions of undeformed oscillators, which are nonlocal in momentum space. The deformations manifest at the multiparticle level, as the one-particle states are identical to the undeformed ones. We successfully introduce a covariant and involutive deformed flip operator using the R matrix. The corresponding deformed (anti-)symmetrization operators are covariant and idempotent, allowing for a well-posed definition of multiparticle states, a result long sought in Quantum Field Theory on $\kappa$-Minkowski. We find that P and T are not symmetries of the theory, although PT (and hence CPT) is. We conclude by noticing that identical particles appear distinguishable in the new theory, and discuss the fate of the Pauli exclusion principle in this setting.

29 pages, 2 figures

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Cited by in corpus (4)

• 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
• Doubly Quantum Mechanics