Statistical mechanics of non-Abelian Chern-Simons particles.

We discuss the statistical mechanics of a two-dimensional gas of nonAbelian Chern-Simons particles which obey the non-Abelian braid statistics. The second virial coefficient is evaluated in the framework of the non-Abelian Chern-Simons quantum mechanics. PACS numbers: 03.65.Bz, 05.30.-d Typeset using REVTEX 1 One of the novel features of anyons [1] is that their thermodynamic character as well as their spin and statistics interpolates between that of bosons to that of fermions as the statistical parameter varies. This feature has been clearly exhibited in the works of Arovas, Schrieffer, Wilczek and Zee [2] where they studied the two-dimensional gas of free anyons in the low-density regime by taking the virial expansion. In particular, the second virial coefficient was evaluated in their study and was found to have periodic, non-analytic behavior as a function of the statistical parameter. Comtet, Georgelin and Ouvry [3] confirmed this result by making use of a harmonic potential as means of a regulator and Blum, Hagen and Ramaswamy [4] discussed further the effects of spin on the second virial coefficient. In this letter, we will discuss the statistical mechanics of a two dimensional gas of SU(2) non-Abelian Chern-Simons (NACS) particles in the framework of the non-Abelian ChernSimons quantum mechanics which has been developed recently in refs. [5–7]. The NACS particles are point-like sources which interact with each others through a topological nonAbelian Aharonov-Bohm interaction. Carrying both non-Abelian charges and non-Abelian magnetic fluxes, they acquire fractional spins and obey braid statistics. Since the braid (non-Abelian) statistics is much more generalized than the fractional statistics of anyons, it is interesting to explore their statistical mechanical properties and to compare them with those of anyons. The NACS particle and the non-Abelian Aharonov-Bohm effect have been discussed in connection with various physical phenomena such as the scattering [8] of nonAbelian vortices which form in some spontaneously broken gauge theories, the fractional quantum Hall effect [9], and the (2+1) dimensional gravity [10]. Thus, exploring the statistical mechanics of the NACS particles is important in many respects. The dynamics of the N -body system of free NACS particles are governed by the Hamiltonian [5,6,11] HN = − N ∑ α=1 1 μα (∇z̄α∇zα +∇zα∇z̄α) ∇zα = ∂ ∂zα + 1 2πκ ∑ β 6=α Q̂aαQ̂ a β 1 zα − zβ (1)