FIRST QUANTIZATION AND BASIC FOUNDATION OF THE MICROSCOPIC THEORY OF SUPERCONDUCTIVITY

Abstract

First quantization approach has been used for the first time to lay the basic foundation of a general theory of superconductivity applicable to widely different solids. To this effect we first analyze the net Hamiltonian, H(N), of N conduction electrons (ces) to identify its universal part, H_o(N) (independent of the specific aspects of a superconductor or a class of superconductors), and then find the states of H_o(N) to conclude that superconductivity originates, basically, from an inter-play between the zero-point force (f_o) exerted by ces on the lattice constituents and its opposing force (f_a) originating from inter-particle interactions which decide the lattice structure. While the lattice, in the state of equilibrium between f_o and f_a, assumes a kind of mechanical strain and corresponding energy, E_s, the entire system (N ces + strained lattice) is left with a net fall in energy by E_g. Obviously, E_g serves as the main source of ce-lattice direct binding and ce-ce indirect binding leading to the formation of (q, -q) bound pairs of ces, -finally found to be responsible for the onset of superconductivity below certain temperature T_c. We find a relation for T_c which not only explains its high values observed for nonconventional superconductors but also reveals that superconductivity can occur, in principle, at room temperature provided the system meets necessary conditions. Our theory has few similarities with BCS model. It provides microscopic basis for the two wellknown phenomenologies of superconductivity, viz., the two fluid theory and Ψ-theory and corroborates a recent idea that superconducting transition is basically a quantum phase transition. Most significantly, this study demonstrates that microscopic theories of a many body quantum system, such as N ces in solids, liquid He, etc., can be developed by using first quantization approach. It also finds reasons for which any approach (viz., second quantization) which uses single particle basis with plane wave representation of particles achieved limited success in concluding a complete, clear and correct understanding of the low temperature properties (such as superconductivity, superfluidity, etc.) of widely different many body quantum systems for the last seven decades.