Quantization of strongly interacting fields

Abstract

While perturbative techniques work extremely well for weakly interacting field theories (e.g. QED), they are not useful when studying strongly interacting field theories (e.g. QCD at low energies). In this paper we review Heisenberg's idea about quantizing strongly interacting, non-linear fields, and an approximate method of solving the infinite set of Tamm-Dankoff equations is suggested. We then apply this procedure to an infinite energy, classical flux tube-like solution of SU(2) Yang-Mills theory and show that this quantization procedure ameliorates some of the bad behaviour of the classical solution. We also discuss the possible application of this quantization procedure to a recently proposed strongly interacting phonon model of High-$T_c$ superconductors.