Experimental Mathematics and Mathematical Physics
David H. Bailey (USA), Jonathan M. Borwein (Australia), David, Broadhurst (UK), Wadim Zudilin (Australia)
TL;DR
This paper discusses how experimental mathematics techniques, like high-precision computation and recognition of numerical values, have been successfully applied to solve complex problems in mathematical physics, including integrals in Ising and quantum field theories.
Contribution
It highlights recent advances in applying experimental mathematics methods to identify key integrals in various areas of mathematical physics.
Findings
Identification of multi-dimensional integrals in Ising theory
Application of high-precision computations in quantum field theory
Successful recognition of numerical values in magnetic spin theory
Abstract
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
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