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Subject of this work is a class of Chern-Simons field theories withnon-semisimple gauge group, which may well be considered as the moststraightforward generalization of an Abelian Chern-Simons field theory. As amatter of fact these theories, which are characterized by a non-semisimplegroup of gauge symmetry, have cubic interactions like those of non-abelianChern-Simons field theories, but are free from radiative corrections. Moreover,at the tree level in the perturbative expansion,there are only two connectedtree diagrams, corresponding to the propagator and to the three vertexoriginating from the cubic interaction terms. For such theories it is derivedhere a set of BRST invariant observables, which lead to metric independentamplitudes. The vacuum expectation values of these observables can be computedexactly. From their expressions it is possible to isolate the Gauss linkingnumber and an invariant of the Milnor type, which describes the topologicalrelations among three or more closed curves.Comment: 16 pages, 1 figure, plain LaTeX + psfig.st

Chern–Simons field theories with non-semisimple gauge group of symmetry