Calculating the infra-red limit of quantum field theory using analyticity of correlation functions

We describe a general method for calculating the infra-red limit of physical quantities in unitary quantum field theories. Using analyticity of Green functions in a complex scale parameter, the infra-red limit is expressed as a contour integral entirely in the ultra-violet region. The infra-red limit is shown to be the limit of the Borel transform of the physical quantity. The method is illustrated by calculating the central charge of the perturbed unitary minimal models and the critical exponents of φ4 theory in three dimensions. We obtain approximate values for the central charge which are very close to the exact values using only a one loop perturbative calculation. For φ4 theory we obtain estimates which are within the errors of other more elaborate approaches.