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Comment: LaTeX2e, 40 pages, 1 Postscript figure, uses package epsfig
Comment: Talk presented by C.T. at the 4th International Conference in Geometry, Thessaloniki, May 1996, 10 pages, Latex
Comment: 36 pages, revised version, appendix added
Comment: 34 pages, 1 figure (eps), LaTeX, amssymb, epsfig
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other differential calculi and introducing an analogue of the Hodge operator on the latter. The general method is illustrated with several examples.
We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (sigma-models or principal chiral models) is then extended to a class of 'noncommutative' harmonic maps into matrix algebras.
Comment: 16 pages, LaTeX, uses amssymb
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