Some exact results in the boson formulation of superconductivity

The boson formulation of superconductivity is derived quite generally without resorting to power-series expansions in the momentum. An exact form for the boson characteristic function is given in terms of the boson energy. An exact equation for the boson energy is also derived. By solving this equation one can compute the boson characteristic function in the entire domain of momentum. This result implies that one can describe spatial variations of the order parameter and of the magnetic field without any practical restriction.