Abstract
Beyond Migdal's theorem, the theoretical study on thestrong coupling superconductivity under the quantizing magnetic fieldin the system of isotropic 3-dimensional electron gas is reported. Thevertex correction is taken into account to the formulation, previouslydeveloped by the present authors in the expression of Dyson-Eliashbergtheory, which appears in J. Phys. Soc. Jpn. 63 (1994) 1465. Under thecondition that Ward-Takahashi identity is exactly satisfied, the setof equations including the vertex correction up to infinite order isproposed in the context of the theoretical investigation by Nambu inPhys. Rev. 117 (1960) 648. Numerical results for demanded strength ofthe field H for the given concentration of the electron density N arepresented in relation with the investigation of the problem of how theNambu-Goldstone mode appears. The possibility of new superconductingphase under the ultra-high field is also discussed.
