Twisted Conformal Algebra so(4,2)

Details Twisted Conformal Algebra so(4,2) Twisted Conformal Algebra so(4,2)

2002-07-25

arxiv.org/abs/hep-th/0207233v1

J.Phys.A35:8179-8196,2002

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX

Scientific paper

10.1088/0305-4470/35/39/304

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.

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