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Low-energy excitations in spin-1 2 antiferromagnetic(AF) Heisenberg spin ladders are studied by bosonization and gauge -theoretical description. The AF Heisenberg models on ladders are described by spin-1 2 fermions and the systems are reduced to relativistic gauge theories of fermions by a mean-field type decoupling and linearization of fermion's dispersion relation near Fermi points. There gauge field is nothing but phase degrees of freedom of "mean field" on links. It is explicitly shown that zero-mode part of boson fields for the bosonization of fermions plays an essentially important role to obtain correct results. In the 2-leg case, the lowest-energy excitations are spin-triplet magnon and they are described by three massive Majorana fermions. On the other hand in the 3-leg system, spin excitations on the top and bottom chains are described by two massless boson fields. It is predicted that if coupling between spins on the top and bottom chains is introduced, a phase transition occures at some critical coupling. Above the critical coupling, the system acquires an energy gap and low-energy excitations are spin-triplet magnon and spin-singlet excitation.

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We introduce an integrable impurity model in which both electrons and impurity have spin and flavour degrees of freedom. This model is a generalization of the multichannel Kondo model and closely related with resonant tunneling through quantum dot. The Hamiltonian is exactly diagonalized by means of the Bethe ansatz.