Symbolic integration with respect to the Haar measure on the unitary groups

• DOI: 10.1515/bpasts-2017-0003
• Publication Date: 2017-02-21T14:26:24Z
• Authors: Z. Puchała; J.A. Miszczak
• Keywords: Computer Science - Symbolic Computation; FOS: Computer and information sciences; Quantum Physics; FOS: Physical sciences; Computational Physics (physics.comp-ph); Symbolic Computation (cs.SC); 68W30 (Primary), 28C10, 97N80 (Secondary); 01 natural sciences; I.1.1; 0103 physical sciences; Quantum Physics (quant-ph); Physics - Computational Physics

Abstract We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.