Vertex Operators - From a Toy Model to Lattice Algebras

Details Vertex Operators - From a Toy Model to Lattice Algebras Vertex Operators - From a Toy Model to Lattice Algebras

1996-11-11

arxiv.org/abs/q-alg/9611010v4

Commun.Math.Phys. 191 (1998) 87-136

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, LaTex. Some corrections made, references added

Scientific paper

10.1007/s002200050263

Within the framework of the discrete Wess-Zumino-Novikov-Witten theory we analyze the structure of vertex operators on a lattice. In particular, the lattice analogues of operator product expansions and braid relations are discussed. As the main physical application, a rigorous construction for the discrete counterpart g_n of the group valued field g(x) is provided. We study several automorphisms of the lattice algebras including discretizations of the evolution in the WZNW model. Our analysis is based on the theory of modular Hopf algebras and its formulation in terms of universal elements. Algebras of vertex operators and their structure constants are obtained for the deformed universal enveloping algebras U_q(G). Throughout the whole paper, the abelian WZNW model is used as a simple example to illustrate the steps of our construction.

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