On a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions

Simple item page
dc.creatorCoffey, Mark W.
dc.date2008-01-01
dc.date2008-01-21
dc.date.accessioned2026-07-07T11:54:56Z
dc.date.available2026-07-07T11:54:56Z
dc.descriptionPerturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C^Tet \equiv C(1,1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially fast convergent sum for C(1,1), as well as a previously empirical relation for C(1,1) as a remarkable difference of Clausen function values. Our presentation includes Propositions extending the theory of the dilogarithm Li_2 and Clausen Cl_2 functions, as well as their relation to other special functions of mathematical physics. The results strengthen connections between Feynman diagram integrals, volumes in hyperbolic space, number theory, and special functions and numbers, specifically including dilogarithms, Clausen function values, and harmonic numbers.
dc.description56 pages, no figures Proposition 10 added, proving another conjecture
dc.identifierhttps://arxiv.org/abs/0801.0273
dc.identifierhttp://arxiv.org/abs/0801.0273
dc.identifierJ.Math.Phys.49:043510,2008
dc.identifierdoi:10.1063/1.2902996
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/205085
dc.subjectMathematical Physics
dc.subject33B30, 33B15, 33C20
dc.titleOn a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions
dc.typetext

Files

Collections

arXiv