Twisted Classical Poincaré Algebras

Details Twisted Classical Poincaré Algebras Twisted Classical Poincaré Algebras

1993-12-09

arxiv.org/abs/hep-th/9312068v1

J.Phys.A27:2389-2400,1994

Physics

High Energy Physics

High Energy Physics - Theory

\Large \bf 19 pages, Bonn University preprint, November 1993

Scientific paper

10.1088/0305-4470/27/7/018

We consider the twisting of Hopf structure for classical enveloping algebra $U(\hat{g})$, where $\hat{g}$ is the inhomogenous rotations algebra, with explicite formulae given for $D=4$ Poincar\'{e} algebra $(\hat{g}={\cal P}_4).$ The comultiplications of twisted $U^F({\cal P}_4)$ are obtained by conjugating primitive classical coproducts by $F\in U(\hat{c})\otimes U(\hat{c}),$ where $\hat{c}$ denotes any Abelian subalgebra of ${\cal P}_4$, and the universal $R-$matrices for $U^F({\cal P}_4)$ are triangular. As an example we show that the quantum deformation of Poincar\'{e} algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincar\'{e} algebra. The interpretation of twisted Poincar\'{e} algebra as describing relativistic symmetries with clustered 2-particle states is proposed.

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