Form Factors in the sine-Gordon Theory

Following the work with Jimbo and Miwa[1], we introduce a certain degeneration of the elliptic algebra Aq,p ( ŝl2 ) and its boson realization. We investigate its rational limit. The limit is the central extension of the Yangian double DY (sl2) at level one. We give a new boson realization of it. Based on these algebras, we reformulate the Smirnov’s form factor bootstrap approach to the sine-Gordon theory and the SU(2) invariant Thirring model. A conjectural integral formula for form factor in the sine-Gordon theory is derived. Talk given at the Nankai-CRM joint meeting on ”Extended and Quantum Algebras and their Applications to Physics”, Tianjin, China, August 19-24, 1996. To appear in the CRM series in mathematical physics, Springer Verlag. † E-mail: [email protected]