Wednesday, June 20, 2012

1206.4150 (D. Chicherin et al.)

Conformal group: R-matrix and star-triangle relation    [PDF]

D. Chicherin, S. Derkachov, A. P. Isaev
The main purpose of this paper is the construction of the R-operator which acts in the tensor product of two infinite-dimensional (differential) representations of the conformal algebra so(p+1,q+1) and solves Yang-Baxter equation. We build this general R-operator as a product of more elementary operators S_1, S_2 and S_3. Operators S_1 and S_3 are identified with intertwining operators of the equivalent irreducible representations of the conformal algebra and the operator S_2 is obtained from the intertwining operators S_1 and S_3 by a certain duality transformation. There are star-triangle relations for the basic building blocks S_1, S_2 and S_3 which produce all other relations for the general R-operators. In the case of the conformal algebra so(p+1,q+1) we construct the R-operator for the scalar (spin part is equal to zero) differential representations and prove that the star-triangle relation is a well known star-triangle relation for propagators of scalar fields. In the special case of the conformal algebra so(2,4) of the 4-dimensional Minkowski space, the R-operator is obtained for more general class of differential representations with nontrivial spin parts. As a result, for the case of the 4-dimensional Minkowski space, we generalize the scalar star-triangle relation to the most general star-triangle relation for the propagators of particles with arbitrary spins.
View original: http://arxiv.org/abs/1206.4150

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