Braided Momentum in the Q-poincare Group
نویسنده
چکیده
The q-Poincaré group of [1] is shown to have the structure of a semidirect product and coproduct B>⊳ ̃ SOq(1, 3) where B is a braided-quantum group structure on the q-Minkowski space of 4-momentum with braided-coproduct ∆p = p⊗ 1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors V (R), V (R) exist for a general R-matrix. The abstract structure of the q-Lorentz group is also studied.
منابع مشابه
BRAIDED MATRIX STRUCTURE OF q-MINKOWSKI SPACE AND q-POINCARE GROUP
We clarify the relation between the approach to q-Minkowski space of Carow-Watamura et al. with an approach based on the idea of 2 × 2 braided Hermitean matrices. The latter are objects like super-matrices but with Bose-Fermi statistics replaced by braid statistics. We also obtain new R-matrix formulae for the q-Poincaré group in this framework.
متن کاملar X iv : m at h / 99 02 14 1 v 1 [ m at h . Q A ] 2 4 Fe b 19 99 Braided Oscillators
A generalized oscillator algebra is proposed and the braided Hopf algebra structure for this generalized oscillator is investigated. Using the solutions for the braided Hopf algebra structure, two types of braided Fibonacci oscillators are introduced. This leads to two types of braided Biedenharn-Macfarlane oscillators as special cases of the Fibonacci oscillators. We also find the braided Hopf...
متن کاملSOME REMARKS ON THE q-POINCARE ALGEBRA IN R-MATRIX FORM
The braided approach to q-deformation (due to the author and collaborators) gives natural algebras R21u1Ru2 = u2R21u1R and R21x1x2 = x2x1R for q-Minkowski and q-Euclidean spaces respectively. These algebras are covariant under a corresponding background ‘rotation’ quantum group. Semidirect product by this according to the bosonisation procedure (also due to the author) gives the corresponding P...
متن کاملQUASI-∗ STRUCTURE ON q-POINCARE ALGEBRAS
We use braided groups to introduce a theory of ∗-structures on general inhomogeneous quantum groups, which we formulate as quasi-∗ Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix form appro...
متن کاملThe Quantum Double as Quantum Mechanics
We introduce ∗-structures on braided groups and braided matrices. Using this, we show that the quantum double D(Uq(su2)) can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski space (a three-sphere in the Lorentz metric), and with the role of angular momentum played by Uq(su2). This provides a new example of a quantum system whose algebr...
متن کامل