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

TL;DR

This paper develops a relativistic quantum field theory on lightlike $$-Minkowski spacetime, introducing a braided algebra for multiparticle states that preserves $$-Poincaré invariance and explores symmetry properties and particle indistinguishability.

Contribution

It constructs a covariant, involutive deformed flip operator and defines multiparticle states in $$-Minkowski QFT, addressing longstanding issues in noncommutative quantum field theories.

Findings

Deformed multiparticle states retain one-particle properties.

P and T symmetries are broken, but PT and CPT are preserved.

Particles become distinguishable, affecting the Pauli principle.

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 $\kappa$-Poincar\'e quantum group of isometries is triangular, and its quantum R matrix enables the definition of a braided algebra of N points that retains $\kappa$-Poincar\'e 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.