Pressure in Chern-Simons Field Theory to Three-Loop Order

TL;DR

This paper computes the pressure of a dilute anyon gas using Chern-Simons field theory up to second order, revealing divergence cancellations near Bose statistics and confirming the hermiticity of the Hamiltonian at this order.

Contribution

It provides a perturbative calculation of the anyon gas pressure to second order, highlighting divergence cancellations and the absence of non-hermitian Hamiltonians at this level.

Findings

Divergences cancel near Bose statistics

No non-hermitian Hamiltonian needed at this order

Pressure computed perturbatively to second order

Abstract

We calculate perturbatively the pressure of a dilute gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory. Near Bose statistics , the divergences in the perturbative expansion are exactly cancelled by a two-body $\delta$-function potential which is not required near Fermi statistics. To the order considered, we find no need for a non-hermitian Hamiltonian. (This paper precedes the article ''Three loop calculation of the full anyonic partition function'', by R. Emparan and M. Valle Basagoiti, hep-th/9304103)