# Fermions in Instanton Anti-Instanton Background

Guida, Riccardo and Konishi, Kenichi (1994) Fermions in Instanton Anti-Instanton Background. International Journal of Modern Physics A, 09 (15). ISSN 1793-656X

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## Abstract

We consider the behaviour of fermions in the background of instanton-anti\-instanton type configurations. Several different physics problems, from the high energy electroweak interactions to the study of vacuum structure of QCD and of large orders of perturbation theory are related to this problem. The spectrum of the Dirac operator in such a background is studied in detail. We present an approximation for the fermion correlation function when the instanton-anti\-instanton separation ($R$) is large compared to their sizes ($\rho$). The situation when the instanton-anti\-instanton overlap and melt, is studied through the behaviour of the Chern Simons number as a function of $R/\rho$ and $x_4$. Applying our results to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical basis for expecting anomalous cross sections to become observable at energies in $10$ TeV region.

Item Type: Article Imported from arXiv Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici Dipartimenti (from 2013) > DIPARTIMENTO DI FISICA dott.ssa Sandra Faita 11 Feb 2014 13:21 11 Feb 2014 13:21 http://eprints.adm.unipi.it/id/eprint/1651

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