Spin Chains and Gustafson's Integrals
S.E. Derkachov, A.N. Manashov
TL;DR
This paper connects Gustafson's integrals to spin chain models using Sklyanin's separated variables, revealing their origin and introducing new integrals in the process.
Contribution
It demonstrates that certain Gustafson's integrals originate from relations in spin chain models and presents several new integrals related to this framework.
Findings
Gustafson's integrals are derived from spin chain matrix element relations
New integrals related to spin chain models are introduced
The connection between integrals and separated variables is established
Abstract
Gustafson's integrals are multidimensional generalizations of the classical Mellin-Barnes integrals. We show that some of these integrals arise from relations between matrix elements in Sklyanin's representation of Separated Variables in spin chain models. We also present several new integrals.
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