On the Fock space for nonrelativistic anyon fields and braided tensor products

TL;DR

This paper constructs a Fock space for nonrelativistic anyon fields using braided tensor products, revealing algebraic structures and exclusion principles that relate to anyonic statistics and enabling computation of the partition function for an ideal gas of vortices.

Contribution

It introduces a braided tensor product framework for anyon Fock spaces, providing a new perspective and tools for analyzing anyonic quantum fields and their statistical properties.

Findings

Realized N-anyon Hilbert spaces as braided-symmetric tensor products.

Derived an anyonic exclusion principle linked to occupation number statistics.

Computed the partition function for an ideal gas of fixed vortices.

Abstract

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category. We see how essential physical information is thus encoded. In particular we show how the algebraic structure of our anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealised gas of fixed anyonic vortices.