Instantons in non-Cartesian coordinates

The multi-instanton solutions of 't Hooft and of Jackiw, Nohl, arid Rebbi a re generalized to the case of curvilinear coordinates. The resulting formul as are considerably simplified if the transformation of coordinates is supp lemented with a gauge transformation. As a result, the gauge Field develops a tern that has the same form as in Cartesian coordinates and which descri bes pseudoparticles and a compensating addition of a geometric origin (it i s determined by the coordinate frame used). The singularities of the compen sating field are irrelevant to physical quantities, but they can affect gau ge-dependent quantities. (C) 2001 MAIK "Naukia/Interperiodica".