A dilogarithmic integral arising in quantum field theory

Details A dilogarithmic integral arising in quantum field theory A dilogarithmic integral arising in quantum field theory

2009-11-19

arxiv.org/abs/0911.3773v1

J. Math. Phys. 50 (2009) 023515

Mathematics

Classical Analysis and ODEs

6 pages

Scientific paper

10.1063/1.3085764

Recently, an interesting dilogarithmic integral arising in quantum field theory has been closed-form evaluated in terms of the Clausen function $\text{Cl}_2(\theta)$ by Coffey [J. Math. Phys.} 49 (2008), 093508]. It represents the volume of an ideal tetrahedron in hyperbolic space and is involved in two intriguing equivalent conjectures of Borwein and Broadhurst. It is shown here, by simple and direct arguments, that this integral can be expressed by the triplet of the Clausen function values which are involved in one of the two above-mentioned conjectures.

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