Theory of Spontaneous Symmetry Breaking and an Application to Superconductivity: Nambu-Goldstone and Higgs Excitation Modes (Communications in Computational Physics, 2018)
We present a general framework of the theory of spontaneous symmetrybreaking in non-relativistic systems. We discuss a spontaneous symmetry breaking ina system with general global symmetry given by a Lie group G. The Nambu-Goldstoneboson and Higgs boson are represented explicitly by local fields by means of the basisof the Lie algebra of G. An application to superconductivity is discussed. We evaluatethe Green's functions of the Nambu-Goldstone and Higgs bosons in superconductors.We show that the Nambu-Goldstone and Higgs modes exhibit interesting behaviors inmulti-component superconductors.