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Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories

Gianluca Mandanici
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Abstract

We apply the Cornwall-Jackiw-Tomboulis (CJT) formalism to the scalar $λϕ^{4}$ theory in canonical-noncommutative spacetime. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter $θ_{μν}$. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case ($θ_{μν}= 0$), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

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Gianluca Mandanici. 2003-04-09. Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories. https://doi.org/10.1142/s0217751x04018270

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