The asymptotics of the correlation functions in (1 + 1)d quantum field theory from finite size effects in conformal theories

Using the finite-size effects, the scaling dimensions and correlation functions of the main operators in continuous and lattice models of 1d spinless Bose-gas with pairwise interaction of rather general form are obtained. The long-wave properties of these systems can be described by the Gaussian model with central charge c = 1. The disorder operators of the extended Gaussian model are found to correspond to some nonlocal operators in the XXZ Heisenberg antiferromagnet. This same approach is applicable to fermionic systems. Scaling dimensions of operators and correlation functions in the systems of interacting Fermi-particles are obtained. This paper presents a universal treatment for 1d systems of different kinds which is independent of the exact integrability and which gives universal expressions for critical exponents through the thermodynamic characteristics of the system