On the Free Energy of Noncommutative Quantum Electrodynamics at High Temperature

Abstract

We compute higher order contributions to the free energy of noncommutative quantum electrodynamics at a nonzero temperature $T$. Our calculation includes up to three-loop contributions (fourth order in the coupling constant $e$). In the high temperature limit we sum all the {\it ring diagrams} and obtain a result which has a peculiar dependence on the coupling constant. For large values of $e\theta T^2$ ($\theta$ is the magnitude of the noncommutative parameters) this non-perturbative contribution exhibits a non-analytic behavior proportional to $e^3$. We show that above a certain critical temperature, there occurs a thermodynamic instability which may indicate a phase transition.

arXiv comment28 pages, 37 figures. Matches published version in Nuclear Physics B

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• Nonanalyticity of the free energy in thermal field theory
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• High temperature limit in static backgrounds
• Noncommutative real scalar field theory in 2+1 dimensions at finite temperature
• On space-time noncommutative U(1) model at high temperature