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Non-commutative solitons. (English) Zbl 0989.81612
Summary: We find classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative field theories whose scalar potential, \(V(\phi)\), has at least two minima. These solutions are bubbles of the false vacuum whose size is set by the scale of noncommutativity. Our construction uses the correspondence between non-commutative fields and operators on a single particle Hilbert space. In the case of noncommutative gauge theories we note that expanding around a simple solution shifts away the kinetic term and results in a purely quartic action with linearly realised gauge symmetries.

81T75 Noncommutative geometry methods in quantum field theory
81T10 Model quantum field theories
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