Large distance expansion in the Schrödinger representation of quantum field theory

Abstract

This thesis is concerned with an approach to Quantum Field Theory in which the states are constructed from their large distance behaviour. The logarithm of the vacuum functional is expandable as a local quantity in any quantum field theory in which the tightest physical particle has a non-zero mass. This local expansion satisfies its own form of the Schrodinger equation from which its coefficients can be determined. We illustrate for ϕ(^4)(_1+1)- theory that our local expansion incorporates correctly the short distance behaviour as contained in the counterterms of the Hamil tonian. A Feynman diagram expansion of the vacuum functional is also presented. The amplitudes are calculated and their large distance expansion are in good agreement with our semi-classical solution of the Schrödinger equation. Some applications of this formalism to the study of the Schrödinger functional are also suggested.