  In the design and investigation of superconducting qubits and related
devices, a lumped element circuit model is the standard theoretical approach.
However, many important physical questions lie beyond its scope, e.g. the
behavior of circuits with strong Josephson junctions carrying substantial
currents and the properties of small superconducting devices. By performing
gauge transformations on self-consistent solutions of the Bogoliubov-de Gennes
equations, we develop here a formalism that treats Josephson couplings
non-perturbatively. We apply the formalism to (a) show that Fermi sea effects
can contribute to the effective capacitance of small charge qubits; (b)
demonstrate an asymmetry in clockwise and counterclockwise current states in
small RF squid qubits; and (c) provide a microscopic wavefunction of
superconducting Schrodinger cats suitable for computing the number of entangled
electrons.
