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aDFTT-39/94November,1994hep-th/9411203ADEfunctionaldilogarithmidentitiesintegrableandmodelsF.GliozziaandR.TateoabaDipartimentodiFisicaTeoricadell’Universit`adiTorinoIstitutoNazionalediFisicaNucleare,SezionediTorino viaP.Giuria1,I–10125Torino,ItalybDepartmentofMathematics,UniversityofDurham Durham,DH13LEEnglandAbstractWedescribeanewin nitefamilyofmulti-parameterfunctionalequationsfortheRogersdilogarithm,generalizingAbel’sandEuler’sformulas.TheyaresuggestedbytheThermodynamicBetheAnsatzapproachtotherenormalizationgroup owof2Dintegrable,ADE-relatedquantum eldtheories.Theknownsumrulesforthecentralchargeofcritical xedpointscanbeobtainedasspecialcasesofthese.

Weconjecturethatsimilarfunctionalidentitiescanbeconstructedforanyrationalintegrablequantum eldtheorywithfactorizedS-matrixandsupportitwithextensivenumericalchecks.