Alternative evaluation of a ln tan integral arising in quantum field theory

Details Alternative evaluation of a ln tan integral arising in quantum field theory Alternative evaluation of a ln tan integral arising in quantum field theory

2008-10-28

arxiv.org/abs/0810.5077v2

Physics

Mathematical Physics

20 pages, no figures, Appendix B added

Scientific paper

A certain dilogarithmic integral I_7 turns up in a number of contexts including Feynman diagram calculations, volumes of tetrahedra in hyperbolic geometry, knot theory, and conjectured relations in analytic number theory. We provide an alternative explicit evaluation of a parameterized family of integrals containing this particular case. By invoking the Bloch-Wigner form of the dilogarithm function, we produce an equivalent result, giving a third evaluation of I_7. We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl_2.

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