Twisted Conformal Algebra so(4,2)

TL;DR

This paper introduces a new twisted quantum deformation of the conformal algebra in four-dimensional spacetime, exploring its algebraic structure, non-relativistic limits, and implications for a discretized spacetime lattice.

Contribution

It presents a novel twisted deformation of so(4,2), supported by an eight-dimensional subalgebra, and explores its non-relativistic limits and associated wave equations.

Findings

Deformation preserves the Weyl-Poincare subalgebra as a Hopf subalgebra.

Non-relativistic limits lead to new twisted Galilean and Carroll conformal algebras.

A difference-differential wave equation with twisted conformal symmetry is constructed.

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.