1996/08/30 by I. Ya. Arefeva, I. Ya. Aref’eva, A. P. Zubarev +3
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Matrix Theory and Algorithms #Theoretical and Computational Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9609007
48 pages, 16 figures, latex, uses bezier.sty
arxiv created 1996/08/30 · openalex publication_date 1996/08/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an interaction representation in the Boltzmann field theory. It describes the master field for a subclass of planar diagrams in matrix models, so called half-planar diagrams. This interaction representation was found in the previous paper by Accardi, Volovich and one of us (I.A.) and it has an unusual property that one deals with a rational function of the interaction Lagrangian instead of the ordinary exponential function. Here we study the interaction representation in more details and show that under natural assumptions this representation is in fact unique. We demonstrate that corresponding Schwinger-Dyson equations lead to a closed set of integral equations for two- and four-point correlation functions. Renormalization of the model is performed and renormalization group equations are obtained. Some model examples with discrete number of degrees of freedom are solved numerically. The solution for one degree of freedom is compared with the planar approximation for one matrix model. For large variety of coupling constant it reproduces the planar approximation with good accuracy.