GAUGE-THEORY BASED UPON SOLVABLE LIE-ALGEBRAS

It has been demonstrated that mathematically consistent Yang-Mills gau ge theories can be constructed on the basis of a class of general Lie algebras called quasiclassical, which contains reductive as well as a class of solvable Lie algebras. However, if we require that these theo ries should be ghost-free, then only the standard gauge theories based upon compact Lie algebras are allowed. Nevertheless, these solvable g auge theories may be relevant for some integrable models based upon th e zero-curvature condition.