A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spacelike κ-Poincaré dual Hopf algebra.
Heisenberg XXZ Model and Quantum Galilei Group
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The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show that the magnon excitations and the s=1/2, n-magnon bound states are determined by the algebra. Thus the Gamma_q(1) symmetry provides a description that naturally induces the Bethe Ansatz. The recurrence relations determined by Gamma_q(1) permit to express the energy of the n-magnon bound states in a closed form in terms of Tchebischeff polynomials.
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Universal $T$-matrices for quantum Poincar\'e groups: contractions and quantum reference frames
A new quantum deformation of the centrally extended Poincaré algebra is introduced whose universal T-matrix contracts to the Galilei T-matrix for quantum reference frames and appears as a central extension of the spacelike κ-Poincaré dual Hopf algebra.