Canonical analysis and symmetries for a nonrelativistic system of anyons

김상준

A. P. Balachandran, T. R. Govindarajan, B. K. Vijayalakshmi

It is known that the equations of motion of a classical system do not in general determine its canonical description uniquely. Thus the corresponding quantum system obtained by canonical quantization is also ambiguous. We use this freedom to quantize a free nonrelativistic particle so that the corresponding quantum particle has half-integral or integral helicity. Methods are developed for finding inequivalent canonical descriptions of a given classical system. It is emphasized that classical symmetries can be broken at the quantum level by a suitable choice of the canonical formalism prior to quantization. It is suggested that this may provide a new mechanism for breaking internal symmetries at the quantum level.

Shiing-Shen Chern, C. W. Chu, C. S. Ting

J. Negro, M. A. del Olmo, Jaromir Tosiek

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincaré and Galilei Maxwell groups. 1

Garth A. Baker, S. B. Mulay

Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume

Nonrelativistic anyons in one dimension possess generalized exchange statistics in which the exchange of two identical anyons generates a phase that is governed by the spatial ordering of the particles and the statistical parameter $\ensuremath{\alpha}$. Working in the continuum, we demonstrate the existence of two distinct types of one-dimensional (1D) anyons, namely, bosonic anyons and fermionic anyons. We identify a many-body Hamiltonian with additive two-body zero-range interactions that supports bosonic and fermionic anyon eigenstates, which are, for arbitrary interaction strength, related through a generalized bosonic-anyon--fermionic-anyon mapping, an extension of the celebrated Bose-Fermi mapping for zero-range interacting 1D systems. The momentum distributions of bosonic and fermionic anyons are distinct: while both feature ${k}^{\ensuremath{-}2}$ and ${k}^{\ensuremath{-}3}$ tails, the associated prefactors differ. Our work reveals intricate connections between the generalized exchange statistics, the universal two- and three-body Tan contacts of systems consisting of $N$ identical particles, and the emergence of statistics-induced chiral symmetry breaking.