Goldstone bosons in the pairing Hamiltonian: The path integral approach

As a first step to derive the interacting boson model from a microscopic nuclear Hamiltonian, we bosonize the pairing Hamiltonian in the framework of the path integral formalism, respecting both the particle number conservation and the Pauli principle. Special attention is paid to the role of the Goldstone bosons. We construct the saddle point expansion which reproduces the sector of the spectrum associated with the addition or removal of nucleon pairs