Alternative evaluation of a ln tan integral arising in quantum field theory
نویسنده
چکیده
A certain dilogarithmic integral I7 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 I7. We also alternatively formulate some conjectures which we pose in terms of values of the specific Clausen function Cl2.
منابع مشابه
Evaluation of a ln tan integral arising in quantum field theory
We analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new representations of the Clausen function Cl2 and the Catalan constant G = Cl2(π/2), as well as new relations between sine and Clausen function values.
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تاریخ انتشار 2008