# zbMATH — the first resource for mathematics

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.

##### MSC:
 81T75 Noncommutative geometry methods in quantum field theory 81T10 Model quantum field theories
Full Text: