Nonuniform symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory

Abstract

The spontaneous symmetry breaking in noncommutative $\lambda {\Phi }^4$ theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase transition to a constant vacuum expectation of the field and the broken phase corresponds to a nonuniform background. By considering $<\varphi (x)>=A\cos (\vec{Q}\cdot \vec{x})$ the generated mass gap depends on the angles among the momenta $\vec{k}$ and $\vec{Q}$ and the noncommutativity parameter $\vec{\theta }$. The order of the transition is not easily determinable in our approximation.

18 pages, 4 figures, added references

References in corpus (1)

• Non--Commutative Field Theories beyond Perturbation Theory

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