Direct construction of path integrals in the lattice-space multiband dynamics of electrons in a solid

It is suggested that complex problems in ultrasubmicrometer electronics research may greatly benefit from use of the path-integral technique. The use of the Weyl-Wigner formalism of the quantum dynamics of electrons in solids provides a rigorous and straightforward derivation of the path integral in solid-state physics, both from the single-particle and from the many-body field-theoretical description of electron dynamics, without the need to postulate a priori the isomorphism between quantum operators and c-numbers of the base field. A rigorous construction of the path integral in many-body solid-state band theory necessitates a two-stage Weyl correspondence between quantum operators and c-numbers of the base field, namely, the Weyl correspondence of the base field of ‘‘lattice-space’’ particle-dynamical variables and that of the continuum many-body field-dynamical variables.