VECTOR STATES FOR SINGLE AND MULTIPLE-POLE RESONANCES

The formulation of quantum mechanics in rigged Hilbert spaces is used to study the vector states for resonance states or Gamow vectors. An i mportant part of the work is devoted to the construction of Gamow vect ors for resonances that appear as multiple poles on the analytic conti nuation of the S-matrix, S(E). The kinematical behavior of these vecto rs is also studied. This construction allow for generalized spectral d ecompositions of the Hamiltonian and the evolutionary semigroups, vali d on certain locally convex spaces. Also a first attempt is made to de fine the resonance states as densities in an extension of the Liouvill e space, here called rigged Liouville space.