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Superconductivity: An Off-Diagonal Long Range Order

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Shigeyuki AONO

Department of Chemistry, Faculty of Science, Kanazawa University

Kanazawa, Ishikawa, 920-1192 Japan

Professor emeritus of Kanazawa University

Present address: Fujiwara 7-41-2-102, Funabashi, 273-0047, Japan

(Received: May 28, 2007; Accepted for publication: August 18, 2008)

In using spinor representation for the electron field, the charge density is given by a 2 × 2 matrix in the spin space. The propagator is also a 2 × 2 matrix. The diagonal term gives the usual many electron problem, and the off-diagonal term gives the superconductive state. The SCF equation for the usual many-electron problem turns out to be the gap equation for the superconductivity problem.

This treatment presents a new theory for the high temperature superconductivity by using the multi-band treatment from which the attractive electron-electron coupling is effectively derived. This coupling is electronic, but not phonon associated. The energy region for making superconductivity possible is a hundred times larger than the phonon frequency.

**Keywords:** Superconductivity, Electron-electron attraction, Nambu spinor, Propagator

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