Abstract
After a short motivation for noncommutativity, a noncommutative (NC) Moyal product is introduced and its’ basic properties are established. Then, the heat kernel expansion for Laplace type operators on the Moyal spaces is constructed. This expansion, together with the results of Chap. 6, is then used to analyse one-loop divergences in NC ϕ 4 theory on the kink background. A short introduction into NC geometry of Connes is presented, and the spectral action for electromagnetic field on the Moyal plane is calculated.
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Fursaev, D., Vassilevich, D. (2011). Noncommutative Geometry and Field Theory. In: Operators, Geometry and Quanta. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0205-9_11
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