Annals of Combinatorics 3 (1999) 287-310


Pseudo-Character Expansions for U(N)-Invariant Spin Models on CPN-1

Attilio Cucchieri1, Tereza Mendes1, and Andrea Pelissetto2, `

1Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
{attilio, mendes}@physik.uni-bielefeld.de

2Dipartimento di Fisica, Università degli Studi La Sapienza di Roma, I-00185 Roma, Italia
 pelissetto@romal.infn.it

Received October 13, 1998

AMS Subject Classification: 20G45, 22E30, 58J15, 82B20

Abstract. We define a set of orthogonal functions on the complex projective space CPN-1, and compute their Clebsch--Gordan coefficients as well as a large class of 6-j symbols. We also provide all the needed formulae for the generation of high-temperature expansions for U(N)-invariant spin models defined on CPN-1

Keywords: σ-model, CPN-1 model, hyperspherical harmonics, spherical functions, Clebsch-Gordan coefficients, 6-j symbols


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