Statistics of the Composite Systems

TL;DR

This paper investigates the commutation relations of composite fields across different dimensions, revealing how atomic and anyonic fields satisfy specific quantum relations, and clarifies the (quasi)particle nature of anyons in fractional quantum Hall systems.

Contribution

It demonstrates that composite atomic and anyonic fields obey their respective commutation relations, providing insights into their (quasi)particle descriptions and the fractional quantum Hall effect hierarchy.

Findings

Atomic fields satisfy canonical commutation relations in the asymptotic limit.

Anyonic fields obey proper anyonic commutation relations with additive phases.

The hierarchy of the fractional quantum Hall effect is explained via (quasi)particle characteristics.

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 composite anyon fields are shown to satisfy the proper anyonic commutation relations with the additive phase exponents. Then, (quasi)particle pictures of the anyons are clarified. The hierarchy of the fractional quantum Hall effect is rather simply nderstood by utilizing the (quasi)particle charactors of the anyons. The commutation relations of the scalar object in the Schwinger(Thirring) model are mentioned briefly.