Superconductivity as Symmetry Breaking. Classical Treatment

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  • Superconductivity as Symmetry Breaking

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The superconductivity is discussed from the viewpoint of the symmetry breaking in the framework of the classical field theory. The classical Schrödinger field of an electron is assumed to be a Grassmann algebra. The interaction with a radiation field is introduced through the gauge field theory. In the Nambu representation, the Lagrangian of the system is invariant under the rotation about the z axis in the spin space, so that the Goldstone theorem suggests that the condensation occurs on the x–y plane. In the absence of any external field, the system is invariant under the phase transformation. This symmetry breaks due to the condensation, and then the massless Goldstone boson which is the supercurrent will follow. The presence of the photon field, however the photon field itself becomes massive due to the gauge symmetry breaking (Higgs phenomenon), which is the Messner effect.

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