THE PRINCIPLE OF MINIMAL SENSITIVITY APPLIED TO A NEW PERTURBATIVE SCHEME IN QUANTUM FIELD THEORY

Abstract

A recently proposed perturbative method for solving a self-interacting scalar φ4 field theory consists of writing the interaction as gφ2(1+δ) and expanding in powers of δ. The method contains an ambiguity in so far as one could modify the interaction Lagrangian by a factor λ(1−δ). The truncated expansion depends on the unphysical parameter, whereas the exact result does not. We exploit this ambiguity by assigning to λ the value for which the truncated result is stationary, thus minimizing its sensitivity to λ. The technique is applied to field theories in zero-and one-dimensional space-times and gives improved accuracy as compared to fixed λ.