A volume formula for asymptotic hyperbolic tetrahedra with an application to quantum field theory

In this paper, a volume formula for hyperbolic tetrahedra with one vertex at infinity is derived. This yields a new representation of the four-dimensional three-point function of Euclidean quantum field theory, i.e., of ∝_R⁴Π³_{k = 1} (q₁² + … + q₄² + b_1kq₁ + … + b_4kq₄ + d_k)⁻¹dq₁…dq₄, through 15 dilogarithms containing inverse trigonometric functions which are symmetric in the parameters b_jk and d_k, j = 1,…,4, k = 1,2,3.