9 research outputs found
Parametrization of semi-dynamical quantum reflection algebra
We construct sets of structure matrices for the semi-dynamical reflection
algebra, solving the Yang-Baxter type consistency equations extended by the
action of an automorphism of the auxiliary space. These solutions are
parametrized by dynamical conjugation matrices, Drinfel'd twist representations
and quantum non-dynamical -matrices. They yield factorized forms for the
monodromy matrices.Comment: LaTeX, 24 pages. Misprints corrected, comments added in Conclusion on
construction of Hamiltonian
Twisted Conformal Algebra so(4,2)
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.Comment: 20 pages, LaTe