Dynamical averages in the dual-resonance model

Abstract

A number of recent papers (1.~) has shown that the methods of statistical mechanics are quite effective in studying the dual-resonance models (DRM). The possibility to use statistical methods is connected with the existence of large resonance spectrum degeneracy in a dual model. We have now to answer the most important question: over what states the averaging is to be performed? The averaging was usually performed over the resonance states, defined by the Fubini-Veneziano factorization. Nevertheless, as shown in ref. (s), the resonance spectrum in diagrams with a finite number of external lines is essentially poorer than the entire spectrum of DRI~I. This circumstance certainly reflects dual-model dynamics and should be taken into account in a statistical treatment (6). In the present paper we introduce a new type of averaging in DRM (the dynamic averaging). The use of this dynamic averaging appears to be quite efficient in studying the physical characteristics in DRM. We base our remark upon the fact that one can clearly construct the resonance states in a dual model, connected with the two basic mesons (hereafter referred to as ::-mesons). Hence, as distinct from the usual averages