Eigenphases of the S-matrix at high energy

In the spirit of a statistical approach to the S-matrix, the authors discuss the concept of resonant state and are led to generalize the eigenphase formalism to many-particle processes. They show that the object to be considered is the connected part of the S-matrix at fixed total four-momentum and they give strong arguments in favour of the conjecture that this operator is compact. This enables them to write a generalized eigenfunction expansion. They define a 'structure function' which describes the distribution of the eigenvalues and study some of its general properties. They consider also some consequences of the assumption that the amplitude is dominated by resonances. (15 refs).