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arXiv · hep-th/0207233

Twisted Conformal Algebra so(4,2)

N. Aizawa·F. J. Herranz·J. Negro·M. A. del Olmo
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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.

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N. Aizawa, F. J. Herranz, J. Negro, M. A. del Olmo. 2002-07-25. Twisted Conformal Algebra so(4,2). https://doi.org/10.1088/0305-4470%2F35%2F39%2F304

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