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Twisted Conformal Algebra so(4,2) | N. Aizawa
; F.J. Herranz
; J. Negro
; M.A. del Olmo
; | Date: |
25 Jul 2002 | Journal: | J.Phys. A35 (2002) 8179-8196 | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | Abstract: | A new twisted deformation, U_z(so(4,2)), of the conformal algebra of the (3+1)-dimensional Minkowskian spacetime is presented. This construction is provided by a classical r-matrix spanned by ten Weyl-Poincare generators, which generalizes non-standard quantum deformations previously obtained for so(2,2) and so(3,2). However, by introducing a conformal null-plane basis it is found that the twist can indeed be supported by an eight-dimensional carrier subalgebra. By construction the Weyl-Poincare subalgebra remains as a Hopf subalgebra after deformation. Non-relativistic limits of U_z(so(4,2)) are shown to be well defined and they give rise to new twisted conformal algebras of Galilean and Carroll spacetimes. Furthermore a difference-differential massless Klein-Gordon (or wave) equation with twisted conformal symmetry is constructed through deformed momenta and position operators. The deformation parameter is interpreted as the lattice step on a uniform Minkowskian spacetime lattice discretized along two basic null-plane directions. | Source: | arXiv, hep-th/0207233 | Services: | Forum | Review | PDF | Favorites |
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