Algebraic quantum field theory

Abstract

Several topics of quantum field theory are discussed within the algebraic context. It is shown that for the charged Bose field there are two natural ways of defining the local field algebras; however, these are relatively antilocal in the sense of Segal and Goodman. We define the charge sectors and show that although they are unitarily inequivalent representations of the observable algebra, they are physically (and, in fact, strongly locally) equivalent. This is a partial justification of the use of abstract algebras. The converse problem, that of constructing charge carrying fields given the observable algebra in the charge zero sector, is then tackled for the case of a massless boson field in two dimensional space time. This is achieved by applying the techniques of Doplicher, Haag and Roberts, viz, the use of localised automorphisms. The specific localised automorphisms used are suggested by consideration of Skyrme's model for zero mass. Finally, we discuss the time evolution co-responding to a bounded interaction density in an arbitrary number of space dimensions. This extends a result of Guenin. A. condition on the interaction in order that the resulting time evolution be causal is given.