English

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

Mathematical Physics 2008-11-15 v2 math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0810.5077,
  title  = {Alternative evaluation of a ln tan integral arising in quantum field theory},
  author = {Mark W. Coffey},
  journal= {arXiv preprint arXiv:0810.5077},
  year   = {2008}
}

Comments

20 pages, no figures, Appendix B added