Vertex Operators  From a Toy Model to Lattice Algebras
Abstract
Within the framework of the discrete WessZuminoNovikovWitten 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 . Throughout the whole paper, the abelian WZNW model is used as a simple example to illustrate the steps of our construction.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1998
 DOI:
 10.1007/s002200050263
 arXiv:
 arXiv:qalg/9611010
 Bibcode:
 1998CMaPh.191...87B
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 49 pages, LaTex. Some corrections made, references added