Iochum's Talk
July-18-11
3:43 PM
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Bicrossproduct structure of $κ$-Poincare group and non-commutative geometry
Shahn Majid, Henri Ruegg
(Submitted on 17 May 1994 (v1), last revised 20 May 1994 (this version, v2))
We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct $U(so(1,3))\cobicross T$. The algebra is a semidirect product of the classical Lorentz group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $\kappa$-Poincar\'e acts covariantly on a $\kappa$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics. 
Comments: 
12 pages. Revision: minor typos corrected
Subjects: 
High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)
Journal reference: 
Phys.Lett. B334 (1994) 348-354
DOI: 
10.1016/0370-2693(94)90699-8
arXiv:hep-th/9405107v2
Submission history
From: [view email] 
[v1] Tue, 17 May 1994 11:36:00 GMT (0kb,I)
[v2] Fri, 20 May 1994 11:12:48 GMT (14kb)
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kappa-Minkowski representations on Hilbert spaces
Alessandra Agostini
(Submitted on 9 Dec 2005 (v1), last revised 15 Jun 2007 (this version, v3))
The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in kappa-Minkowski spacetime in terms of the usual trace of operators. 
Comments: 
23 pag. Latex, correction of a couple of typos, reference added, title slightly changed
Subjects: 
High Energy Physics - Theory (hep-th)
Journal reference: 
J.Math.Phys.48:052305,2007
DOI: 
10.1063/1.2738360
arXiv:hep-th/0512114v3
Submission history
From: Alessandra Agostini [view email] 
[v1] Fri, 9 Dec 2005 21:29:56 GMT (22kb)
[v2] Wed, 13 Jun 2007 20:35:01 GMT (21kb)
[v3] Fri, 15 Jun 2007 10:08:12 GMT (21kb)
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