Self-Consistency Equations for Composite Operators in Models of Quantum Field Theory

Abstract

The technique of functional Legendre transforms is used to develop an effective method for calculating the characteristics of critical phenomena in quantum field theory models in the Euclidean space of dimension d. Based on the diagrammatic representation of the second Legendre transform in the theory with a cubic interaction potential, the construction of self-consistent equations is carried out, the solution of which makes it possible to find the dimensions not only of the main fields, but also of the quadratic on the composite operators within the 1/n-expansion. Application of the proposed methods in the model F has given the opportunity to calculate in the main approximation by 1/n the anomalous dimensions of both scalar and tensor composite operators quadratic on the fields ϕ. For them, as functions of the spatial dimension d, we obtained explicit analytical expressions in the form of relations of two polynomials with integer coefficients.