Solvable Models and Mathematical Aspects of Conformal Field Theory

Abstract

The thesis can be divided into two parts. The first part was on Solvable Models and the second on mathematical formulation of CFT. In the first part, we studied different solvable models and the methods used to solve them. We then focused on the 8-Vertex model and explored a novel technique of generating ansatz for the 8-vertex model. Through this technique, we managed to arrive at the two general solutions of the 8-Vertex model. However, despite signifcant efforts, a new solution could not be obtained. We then tried to study [10], which claims that all solutions to the 16-Vertex model can be expressed in terms of the two solutions of the 8-Vertex model, which we previously derived. The results of this paper could not be reproduced. However, we point out some ambiguities in it, and the techniques we used to try to reach the results claimed in it. The second part, on CFT, is based on [12]. Here, we study Conformal Transformation, Quantization of Symmetries, lifting Projective Representation to Unitary Representation(Bargmann's Theorem) and show that Virasoro Algebra is the non-trivial central extension of Witt Algebra.