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Vacuum configurations for renormalizable non-commutative scalar models. (English) Zbl 1189.81213

Summary: We find non-trivial vacuum states for the renormalizable non-commutative \(\varphi ^{4}\) model. An associated linear sigma model is then considered. We further investigate the corresponding spontaneous symmetry breaking.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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