Many-Particle Approach to the One-Electron Problem in Insulators and Semiconductors

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Abstract
A formal theory of one-electron states in insulators and semiconductors is developed from a many-particle point of view. The techniques of second quantization are utilized for this purpose in a manner analogous to that introduced recently for the study of Fermi liquids, i.e., by the study of matrix elements of the electron field operator which describe the propagation of particles or holes. Both types of motion are described symmetrically by means of the one-particle Green's function or propagator. The utility of these constructs for the present study derives from the existence of a gap against single-particle excitation.