Critique of optical transition theories based on projection and population criteria

Abstract

Some many-body theories of optical transitions in solids were examined from projection and population criteria. The results showed that state-independent projection methods cannot be applied to electron systems with non-uniform energy spectra. Moreover, neglecting some important terms in a second-order approximation leads to invalidation of the population criterion. In addition, a valid theory satisfying these two criteria can be obtained using a proper state-dependent projection operator and Kang-Choi reduction identity, and the result can be interpreted using a diagram, which can model the quantum dynamics of electron in solids.