How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. I

Abstract

The new method proposed previously for solving the covariant operator formalism of quantum Einstein gravity is applied to quantum electrodynamics as an exercise of the application to quantum chromodynamics. The purposes of doing this are to establish the details of the method and to reconfirm the validity of the method. The Wightman functions are explicitly constructed, at tree and one-loop levels, so as to be consistent with four-dimensional multiple (anti)commutators and with the energy-positivity condition.