Quantum Sine-Gordon Equation and Quantum Solitons in Two Space-Time Dimensions

Abstract

First a warning: The main emphasis of the “International School of Mathematical Physics, 1975” at Erice was clearly on renormalized perturbation theory in the framework of renormalizable quantum field theories which, one hopes, may be relevant for the physics (not only the mathematics) of quantized fields and elementary particles. Participants of this school wanted to learn something non-trivial about: ultraviolet renormalization, infrared power counting, the strong adiabatic limit (i.e. the construction of the scattering matrix), composite fields, Yang-Mills theories, etc. In my lectures, however, I study mainly the construction and the detailed properties of a new model of a self-interacting, relativistic scalar Bose field in two space- time dimensions: the quantum sine-Gordon equation (≡ s-G theory).