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Induced gauge theory on a noncommutative space
Author(s) -
Wohlgenannt M.
Publication year - 2008
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200710533
Subject(s) - noncommutative geometry , gauge theory , scalar (mathematics) , scalar field theory , action (physics) , physics , effective action , introduction to gauge theory , mathematical physics , supersymmetric gauge theory , theoretical physics , hamiltonian lattice gauge theory , scalar field , space (punctuation) , gauge anomaly , euclidean space , mathematics , quantum mechanics , computer science , pure mathematics , geometry , quantum , quantum gravity , operating system
We discuss the calculation of the 1‐loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar ϕ 4 model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1‐loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model.