Transport equation and hard thermal loops in noncommutative Yang-Mills theory

Abstract

We show that the high temperature limit of the noncommutative thermal Yang-Mills theory can be directly obtained from the Boltzmann transport equation of classical particles. As an illustration of the simplicity of the Boltzmann method, we evaluate the two- and the three-point gluon functions in the noncommutative $U(N)$ theory at high temperatures T. These amplitudes are gauge invariant and satisfy simple Ward identities. Using the constraint satisfied at order ${T}^{2}$ by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory.