Distribution of instanton sizes in a simplified instanton gas model
Institut für Theoretische Physik I, Universität Münster,
Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
Received: 15 May 2000 / Revised version: 17 July 2000 /
Published online: 25 September 2000 - © Springer-Verlag 2000
We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. In one dimension exact results can be derived. In any dimension we find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.
Copyright Società Italiana di Fisica, Springer-Verlag 2000