Nonuniform symmetry breaking in noncommutative lambda phi**4 theory

Spontaneous symmetry breaking in noncommutative cutoff 𝜆⁢𝛷4 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 〈𝜑⁡(𝑥)〉 =𝐴⁢cos⁡( → 𝑄 ⋅ → 𝑥 ) the generated mass gap depends on the angles among the momenta → 𝑘 and → 𝑄 and the noncommutativity parameter → 𝜃 . The order of the transition is not easily determinable in our approximation.