TL;DR
This paper introduces a simplified path representation for RSOS models that facilitates the derivation of fermionic characters and links to sine-Gordon model particles.
Contribution
It presents a new path transformation for RSOS models that simplifies weight calculation and enables fermionic character derivation and particle interpretation.
Findings
New path representation with horizontal edges at certain heights.
Constructive derivation of fermionic characters for specific parameters.
Relation established between RSOS particles and sine-Gordon model excitations.
Abstract
We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p',p). This representation is obtained by transforming the RSOS paths, for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is nothing but the sum of the position of the peaks. This description paves the way for the interpretation of the RSOS paths in terms of fermi-type charged particles out of which the fermionic characters could be obtained constructively. The derivation of the fermionic character for p'=2 and p=kp'+/- 1 is outlined. Finally, the particles of the RSOS paths are put in relation with the kinks and the breathers of the restricted sine-Gordon model.
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