Umklapp frustration and field-theoretic approach to superconductivity

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The formula of Gell-Mann and Low can be applied to both the Stark effect and superconductivity. The standard version of the field-theoretic approach fits the Stark effect, because in this version electrons have identical initial and end states, so that the energy of each and every electron orbit acquires a shift in the same direction. A preliminary alternative version of the field-theoretic approach is introduced, in which the electrons have different initial and end states, to accommodate superconductivity. Consequently the energy of the electrons acquires a random shift, which will cancel macroscopically, unless the electrons are paired. It also becomes apparent that superconductivity is frustrated when normal and umklapp scattering coexist.