Alternative evaluation of a ln tan integral arising in quantum field theory
Abstract
Description
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.
20 pages, no figures, Appendix B added
20 pages, no figures, Appendix B added