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

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 T2 by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory