Abstract
Three-dimensional topological field theoriesassociated with the three-dimensional version of Abelianand non-Abelian Seiberg–Witten monopoles arepresented. These three-dimensional monopole equationsare obtained by a dimensional reduction of thefour-dimensional ones. The starting actions to beconsidered are Gaussian types with random auxiliaryfields. As the local gauge symmetries with topologicalshifts are found to be first-stage-reducible, theBatalin–Vilkovisky algorithm is suitable forquantization. Then the BRST transformation rules areautomatically obtained. Nontrivial observablesassociated with Chern classes are obtained from the geometricsector and are found to correspond to those of thetopological field theory of Bogomol'nyimonopoles.
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