Comment on "Statistical mechanics of non-abelian Chern-Simons particles"

The second virial coefficient B2(T ) for particles which interact with each other through a Chern-Simons type coupling has been of considerable interest in recent years. In particular its form has been derived for both the spin zero [1] and spin-1/2 cases [2] as a function of the flux parameter α. More recently results have been obtained for the case of a gas of spinless non-Abelian Chern-Simons particles. [3] It is the purpose of this note to point out that the form of the virial coefficient obtained in that work for the SU(2) case is quantitatively incorrect and also that there exists a periodicity in the flux parameter just as in the Abelian theory. No such periodicity was noted in ref. 3. To demonstrate the result one can begin with Eq. (25) of ref. 3 which reads