The condensate $\langle\operatorname{tr}(A_\mu^2)\rangle$ in commutative and noncommutative theories

We show that the gauge invariance of the operator$\int dx\,\operatorname{tr}(A_\mu^2- 2/(g\xi)x^\nu\theta_{\mu\nu}A^\mu)$ in a noncommutative gauge theory does not lead to the gauge independence of its vacuum condensate. We obtain the generalized Ward identities for Green's functions containing the operator $\lim_{\Omega\to\infty}(1/\Omega)\int_\Omega dx\,\operatorname{tr}(A_\mu^2)$ in commutative and noncommutative gauge theories.