Preprint/Report

PUBDB-2019-03039

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png On complex Gamma function integrals

Derkachov, S. E. ; Manashov, A. N. (Corresponding author)Extern*

2019

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Please use a persistent id in citations: doi:10.3204/PUBDB-2019-03039

Report No.: DESY-19-116; arXiv:1908.01530

Abstract: It was observed recently that relations between matrix elements of certain operators in the $\text{SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with $\text{SL}(2,\mathbb C)$ symmetry group and $\text{L}_2(\mathbb C)$ as a local Hilbert space give rise to a new type of $\Gamma$-function integrals. In this work we present a direct calculation of two such integrals. We also analyse properties of these integrals and show that they comprise the star--triangle relations recently discussed in the literature. It is also shown that in the quasi-classical limit these integral identities are reduced to the duality relations for Dotsenko-Fateev integrals.

Keyword(s): spin: chain ; higher-dimensional ; Hilbert space ; duality ; magnet

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Contributing Institute(s):

1. Uni Hamburg / Theorie (UNI/TH)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF3-611) (POF3-611)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2019

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Database coverage:
; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Report/Journal Article Derkachov, S. E. (Corresponding author) ; Manashov, A. N. (Corresponding author)Extern*
On Complex Gamma-Function Integrals
Symmetry, integrability and geometry: methods and applications 16, 003 (2020) [10.3842/SIGMA.2020.003]2020     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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