Field theoretic operators for the charge, rho, and current J, densities of the electron gas were obtained using the Darwin Hamiltonian in 'second quantized' form.Temperature dependent Green's functions were formed from certain averaged combinations of the field creation and annihilation operators.Equations of motion were obtained for these Green's functions, and rho and j were written in terms of the Green's functions. In order that rho and j might be expressed explicitly in terms of the perturbing field, formal functional series expansions were obtained for rho and j in terms of the potentials.Connecting relations obtained from the requirements of gauge invariance and charge conservation were used to show the general result that rho and j reduce to functionals of the electric field alone.(Author Modified Abstract).

Excerpt from Quantum Field Theoretic Techniques and the Electromagnetic Properties of an Uniformly Magnetized Electron Gas: Submitted as a Thesis to the University of Colorado in Partial Fulfillment of the Requirements for the Ph. D. Degree Formal functional relations are derived for the charge and current densities of macroscopic systems acted upon by electromag netic fields. Quantum field theoretical techniques are combined with the results of equilibrium statistical mechanics for a many-body theory of the electromagnetic properties of a uniformly magnetized electron gas in the non-relativistic limit. The functional relations for charge and current density are utilized for the case of an additional electromagnetic disturbance acting upon the electron gas. The results comprise a theory of charge transport and electromagnetic fluctuations for the electron gas. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.