Some Aspects of Non-Perturbative Quantum Field Theory (original) (raw)

1996

Abstract

The aim of this thesis is to describe some different ways in which non-perturbative methods enter in quantum field theory. In the thesis such methods enter in 1+1-dimensional theories: various Yang-Mills theories and electrodynamics. It also enters when treating charged bosons or fermions interacting with an external, classical field. In all these cases the interaction is treated exactly and we do not have to rely on perturbation theory. A good foundation for starting non-perturbative investigations in quantum field theory is a functional representation for the (canonical) algebra of the field operators. Such a representation is introduced and illustrated by various examples, mainly free fields and free fields coupled to external fields. The functional representation is well suited for a discussion of equilibrium quantum statistical mechanics by means of a density matrix. This is discussed in various examples. A non-equilibrium problem is also considered in the treatment of external...

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