Dressed skeleton expansion in (1+1)-dimensional field-theory models.

We discuss the implementation of the Dressed Skeleton Expansion (DSE) and analyse various features of this perturbative calculational method in simple field theory models in 1 + 1 dimension. In particular, we investigate issues concerning loop skeleton diagrams, renormalization in the massive case, and the usage of DSE for vertices involving matrix structures. Submitted to Physical Review D * Work supported by the Department of Energy, contract DE-AC03-76SF00515. In a previous paperjwe have pointed out that the Dressed Skeleton Expansion (DSE) offers a calculational method in perturbative quantum field theories without scale ambiguity problem. In particular, we illustrated the usage of the method for +3 theory in six dimensions. The basic motivation in choosing this theory resides in its resemblance with Quantum Chromodynamics (&CD) in the aspects of both being renormalizable theories and presenting asymptotic freedom. However, the high dimensionality of the theory hampered the discussion of higher order skeleton graphs. In this paper we study the application of the DSE to field theories models in 1 + 1 dimension. Our purpose is to analyse and discuss the various features and technical details for the implementation of the DSE method, by using simple models as testground. It is not our goal to obtain new results in these simple field theory models, for there exists abundant literature on the subject.2’3 This paper is organized in the following five sections. In section I, we review briefly the general scale setting problem in quantum field theories, and present the DSE as a scale-ambiguity-free calculational method. In section II we apply the DSE method to massless Gross-Neveu model in leading l/N expansion, and show that DSE leads to exact four-fermion vertex function, no matter whether we choose to dress up the charged two-point function or the three-point function. In section III we apply the DSE method to the massless Thirring model. Here we offer an explicit example of a non-trivial loop skeleton diagram, showing that ‘it indeed can be done and yields a finite result, despite the singularity of the