High-energy behaviour in a non-Abelian gauge theory ; 1, T$_{n --> m }$in the leading ln s approximation

This is the first part of an attempt to find a unitary high-energy description of a spontaneously broken non-Abelian gauge theory. The author calculates the high-energy behaviour of n to m amplitudes in the leading ln s approximation. The author starts from tree approximations and then only use dispersion relations and unitarity equations for elastic and inelastic amplitudes in the multi-Regge limit. The resulting amplitudes have multi-Regge behaviour with simple pole exchange, and satisfy s-channel unitarity in all channels. There is, however, no vacuum quantum number exchange (pomeron) in this approximation. The author briefly outlines a scheme which may lead to a unitary description of the pomeron. (17 refs)