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Gustafson integrals for $SL(2,\mathbb{C})$ spin magnet

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arxiv 1612.00727 v1 pith:VGIS5HST submitted 2016-12-02 math-ph hep-thmath.MP

S.E. Derkachov , A.N. Manashov , P.A. Valinevich This is my paper · ORCID
classification math-phhep-thmath.MP
keywords integralsgustafsonspinmathbbanalysisarisecasechain
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abstract

It was observed recently that the multidimensional Mellin--Barnes integrals (Gustafson's integrals) arise naturally in studies of the $SL(2,R)$ spin chain models. We extend this analysis to the noncompact $SL(2,\mathbb{C})$ spin magnets and obtain integrals which generalize Gustafson's integrals to the complex case.

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  1. On Complex Gamma-Function Integrals

    math-ph 2019-08 conditional novelty 6.0 of 10

    Two complex gamma-function integral identities are proved directly and shown to imply star-triangle relations and the Dotsenko-Fateev duality in a classical limit.

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