Exclusion Statistics: From Pauli to Haldane[MatSciRep: 120]

Abstract

Quantum statistics provides a way of understanding the statistical mechanics of particles whose dynamical evolution is inherently governed by quantum mechanics. The statistics of all observed particles are covered by the two well known realisations of quantum statistics, namely, the Bose-Einstein (BE) statistics and the Fermi-Dirac (FD) statistics. Particles that obey these statistics are called bosons and fermions respectively. While this is true for all elementary particles which can have arbitrarily large momenta and exist in asymptotically free states, in recent years there has been much interest in the physics of “quasi-particles” obeying fractional statistics. Such quasi-particles may correspond to an elementary excitations that can only exist in the interior of a many body interacting system. The discussions in this report include many aspects of Fractional Exclusion Statistics (FES). The central ideal of Fractional Exclusion Statistics(FES), that it provides a frame-work to describe in a rather simple way a certain class of strongly interacting systems is developed further. There may be many important contributions which may not be covered in these pages. What is included is partly based on Authors' understanding of what is important in this field and partly due to their own work forming the basis of this presentation. Obviously it is almost impossible to cover all the of work in Fractional Exclusion Statistics(FES) that has followed Haldane’s seminal work. If some work of importance in the field is left out it is partly due to our ignorance or lack of understanding.