This article is cited in 1 paper

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

R. N. Baranov^a, D. V. Bykov^a, A. A. Slavnov<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Physics
^b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.

Keywords: vacuum condensates, noncommutative field theory, quantum chromodynamics, confinement phase.

Received: 27.02.2006

DOI: 10.4213/tmf2321

 English version: Theoretical and Mathematical Physics, 2006, 148:3, 1168–1173

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