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Covariant particle statistics and intertwiners of the \(\kappa \)-deformed Poincaré algebra. (English) Zbl 1234.81091

Summary: To speak about identical particles-bosons or fermions-in quantum field theories with \(\kappa\)-deformed Poincaré symmetry, one must have a \(\kappa\)-covariant notion of particle exchange. This means constructing intertwiners of the relevant representations of \(\kappa\)-Poincaré. We show, in the simple case of spinless particles, that intertwiners exist, and, supported by a perturbative calculation to third order in \(\frac{1}{\kappa}\), make a conjecture about the existence and uniqueness of a certain preferred intertwiner defining particle exchange in \(\kappa\)-deformed theories.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T99 Quantum field theory; related classical field theories
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