Covariant particle exchange for κ-deformed theories in dimensions

Abstract

We consider the exchange of identical scalar particles in theories with κ-deformed Poincaré symmetry. We argue that, at least in 1+1 dimensions, the symmetric group S N can be realized on the space of N -particle states in a κ-covariant fashion. For the case of two particles this realization is unique: we show that there is only one non-trivial intertwiner, which automatically squares to the identity.

On κ-deformation and triangular quasibialgebra structure

“…We can now make contact with the perturbative results for states of three scalar particles of mass m (transforming in V m ) given in the appendix of [7]. It was shown there that to O(κ −3 ) there exists a one-parameter family of pairs of maps…”

“…of individual constituent particles of a tensor product state. 7 To interact p with q is the first step in the process…”

“…This paper is a continuation of earlier work [6,7], following [8], whose aim is systematically to construct κ-deformed quantum field theory from the following particular perspective. (Other approaches can be found in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].)…”

Deformation Quasi-Hopf Algebras of Non-semisimple Type from Cochain Twists

“…This structure provides the isomorphisms required to make the category of representations a tensor category. As emphasized in [4] -see also [5,6] -apart from the obvious mathematical interest, the extension of this result to non-semisimple Lie algebras would provide a covariant notion of multiparticle states in quantum field theories based on certain deformations of the Poincaré symmetry. Unfortunately, the proof of this result relies crucially on the vanishing of a certain cohomology module, which holds for semisimple Lie algebras but may fail for non-semisimple Lie algebras.…”

“…The map ξ is thus a 1-cocycle of Z 1 (g, Ug ⊗ Ug) in the sense of the Chevalley-Eilenberg complex 6 . As g is semisimple, it follows from lemma 4.2 that the cohomology module H 1 (g, Ug ⊗ Ug) is empty.…”