The Existence of Anyons

Ijaz Durrani

M. V. N. Murthy, J. Law, R. K. Bhaduri +1 more

In the many-anyon problem in two space dimensions, irregular but square integrable solutions of the Schrodinger equation may exist. A class of such solutions is constructed for anyons confined in a harmonic oscillator. It is shown that these may have lower energies than the usual regular solutions, but they do not exist throughout the range between the bosonic and fermionic limits, and as such do not interpolate continuously.

Diptiman Sen

Subir Ghosh

A new model for anyon is proposed, which exhibits the classical analogue of the quantum phenomenon - Zitterbewegung. The model is derived from existing spinning particle model and retains the essential features of anyon in the non-relativistic limit.

E. Westerberg

Klil H. Neori

This dissertation reports our investigation into the existence of anyons, which interpolate between bosons and fermions, in light of the Symmetrization Postulate, which states that only the two extremes exist. The Symmetrization Postulate can be understood as asserting that there are only two consistent ways of combining the behavior of distinguishable particles to obtain the behavior of identical ones. We showed that anyonic behavior then arises because of the way in which the probability amplitudes of distinguishable particles in two dimensions are affected by the topology of the space. These can then be combined in one of the ways arising from the Symmetrization Postulate, to form identical anyons. Therefore, anyons do not invalidate the Symmetrization Postulate, but are entirely compatible with it. In order to show that anyons can arise without particle identity, we investigated how distinguishable particles can gain particular properties from the topology of their configuration space. We managed to do so, and in the process, discovered a novel approach for quantizing multiply-connected spaces, in a way that is more suited to anyons than the standard approach.