A fast C++ implementation of thermal functions

Abstract

We provide a small C++ library with Mathematica and Python interfaces for computing thermal functions, defined JB/F(y2)≡ℜ∫0∞x2log1∓e−x2+y2dx,which appear in finite-temperature quantum field theory and play a role in phase-transitions in the early Universe, including baryogenesis, electroweak symmetry breaking and the Higgs mechanism. The code is available from https://github.com/andrewfowlie/thermal_funcs. Program summaryProgram title: thermal_funcsProgram Files doi: http://dx.doi.org/10.17632/5nzrr2jjpd.1Licensing provisions: BSD 3-ClauseProgramming language: C++, C interface to Mathematica and SWIG interface to PythonNature of problem: Thermal functions appear in finite-temperature quantum field theory and influence phase transitions in the early Universe. They have no closed-form solution. Studying phase transitions requires repeated evaluations of, inter alia, thermal functions. We provide several fast and accurate methods, and first and second derivatives.Solution method: We implement numerical quadrature, a Bessel function representation, asymptotic solutions expressed in terms of zeta functions and polylogarithms, and approximations and limits.