MANIFESTLY FINITE PERTURBATION-THEORY FOR THE SHORT-DISTANCE EXPANSION OF CORRELATION-FUNCTIONS IN THE 2-DIMENSIONAL ISING-MODEL

We review and apply the recently proposed formalism for the study of the theory space of euclidean quantum field theories based on the variational formula to the analysis of the scaling limit of the two-dimensional massive Ising model. An extension of the first-order variational formula to higher orders provides a manifestly finite scheme for the perturbative calculation of the operator product coefficients to any order in parameters. A perturbative expansion of the correlation functions follows. We implement this scheme for a systematic study of correlation functions involving two spin operators. We show how the necessary non-trivial integrals can be calculated. As two concrete examples we explicitly calculate the short-distance expansion of the spin-spin correlation function to third order and the spin-spin-energy-density correlation function to first order in the mass. We also comment on how our results may be applied to perturbations of non-trivial fixed points corresponding to other unitary minimal models.