Non-Grassmann path integral theory for momentum specified photoemission and light absorption spectra of many-electron system with strong long range Coulomb repulsion

Abstract

A new path integral theory for many-electron systems with strong inter-electron repulsions is formulated by the equation of motion method, without using the conventional Grassmann algebra. The repulsions of arbitrary spatial extent are shown to be reduced to a simple time-dependent one-body potential through the path integral over a c-number field, resulting in quantum fluctuations of spins and charges. To evaluate multi-body Green’s functions of this fluctuating system, the ordinary Bloch–De Dominicis theorem is extended so that it can be used even in the cases where the original one-body Hamiltonian is time-dependent, as well as in the well known cases with no time-dependence. Using this theorem, the momentum specified photoemission and the light absorption spectra are calculated, and compared successfully to the experiments on the one- and two-dimensional SDW states of Ni–Br and Cu–O compounds. The origin of serious differences between the photoemission and the light absorption spectra is clarified with a good agreement with these experiments. The reason why the coherent one-body component is absent in the momentum specified photoemission spectrum is also clarified in connection with the strong quantum fluctuation.