Statistics of the Composite Systems and Anyons in the Fractional Quantum Hall Effect

TL;DR

This paper explores the statistical properties and commutation relations of composite fields and anyons in various dimensions, providing insights into the fractional quantum Hall effect and the nature of quasiparticles.

Contribution

It demonstrates that composite anyon fields satisfy proper anyonic commutation relations and clarifies the quasiparticle picture in the fractional quantum Hall effect.

Findings

Composite anyon fields obey proper anyonic commutation relations.

Quasiparticle picture of anyons explains the hierarchy of the fractional quantum Hall effect.

Differences between field and particle aspects are prominent in two dimensions.

Abstract

The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock-space of the atom. The field-particle duality in the bound state is discussed from the statistics point of view. Then, the commutation relations of the scalar object in the Schwinger(Thirring) model are mentioned briefly and are shown consistent with its interpretation as the Nambu-Goldstone boson. The composite anyon fields are shown to satisfy the proper anyonic commutation relations with the additive phase exponents. Then, quasiparticle picture of the anyons is clarified under the restriction of this additibity. The difference between field and particle aspects becomes more prominent in the 2 space dimension. It is argued that the hierarchy of the fractional quantum Hall effect is rather simply understood by utilizing the quasiparticle charactors of the anyons when the background-boson gauge is assumed. In contrast to it, the coposite fermion theories are critically reviewed