Bulg. J. Phys. vol.35 no.s1 (2008), pp. 277-292



Noncommutative Quantum Field Theory

Harald Grosse1, Michael Wohlgenannt2
1University of Vienna, Faculty of Physics, Boltzmanngasse 5, A-1090 Vienna, Austria
2Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Vienna, Austria
Abstract. Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. This disease can be cured by adding one more marginal operator to the Lagrangian, an oscillator potential. We review these ideas and apply them to φ3 models. Then, we study gauge theories on θ-deformed Euclidean space. One approach utilizes the heat kernel expansion method for a scalar field theory coupled to an external gauge field. The other approach constructs a BRST invariant model. Both approaches involve an oscillator potential for the gauge field.

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