Quantum field theory is a theory in physics that is widely used to describe physical phenomena in small scale. Despite its success in physics, it still lacks complete mathematical foundation and it is an important task of mathematics in 21st century to give a foundation to quantum field theory to ensure its validity. In this project, we make a step towards achieving this task. In particular, we study conformal field theory in two dimensions, which forms a special class of quantum field theory. Our approach is to construct a conformal field theory as a continuous limit of discrete systems thereby providing a mathematical foundation to the theory. This approach has been done for the so-called critical Ising model, but in this project, we extend the previous result to more general situations.

2025

2029