On the Quantisation of Topological Field Models

This book deals with the quantisation of topological quantum field theories in 1+1 space-time dimensions. These quantum field theories are the Thirring model and the sine–Gordon model. The Thirring model is a fermionic quantum field theory, which is exactly solvable and hence an interesting laboratory to study quantum effects in a non-perturbative way. While it is well known that the massive Thirring model is renormalisable, the massless model was thought to be non-renormalisable. Here, a more general solution to the massless Thirring model is obtained, which allows to renormalise the massless Thirring model for the first time. The second part deals with the sine–Gordon model. This soliton model is exactly solvable and equivalent to the massive Thirring model. Using path integral techniques the quantum correction to the mass of a soliton is calculated in continuous space–time and within the discretisation technique with periodic and anti-periodic boundary conditions and rigid walls. Finally, it is shown that the finite contribution to the quantum mass of a soliton found in the literature arises due to a non–covariant procedure.