Finite gauge theory on fuzzy image Original Research Article

We give a non-perturbative definition of image gauge theory on fuzzy image as a multi-matrix model. The degrees of freedom are 8 Hermitian matrices of finite size, 4 of which are tangential gauge fields and 4 are auxiliary variables. The model depends on a non-commutativity parameter image, and reduces to the usual image Yang–Mills action on the 4-dimensional classical image in the limit image. We explicitly find the monopole solutions, and also certain image instanton solutions for finite N. The quantization of the model is defined in terms of a path integral, which is manifestly finite. An alternative formulation with constraints is also given, and a scaling limit as image is discussed.