Molecular quantum electrodynamics in the Heisenberg picture: A field theoretic viewpoint

Quantum electrodynamics (QED) is the physical theory that describes the interaction of electrons and photons at a fundamental level. Its characteristic feature is that the radiation field, as well as the system of material particles, obeys the Postulates Of quantum mechanics. A rigorous non-relativistic formulation of this theory applicable to atoms and molecules has also been developed and applied with outstanding Success to a number of processes of interest to chemical physicists, being most commonly explicated for a system of charged particles coupled to the electromagnetic field, with the latter second quantized. Calculations are Subsequently carried Out in the Schrodinger picture. In the last twenty-five years or so, considerable work Oil Coulomb gauge QED of molecules has been performed in the Heisenberg representation of quantum mechanics by adopting a completely field theoretic point of view. The methods and results Of this approach, which offer significant advantages over conventional perturbative techniques for the solution of a number of problems, are reviewed. Beginning with the second quantized Multipolar Hamiltonian, the Heisenberg equations of motion for the fermion and boson creation and annihilation operators are obtained. In the electric dipole approximation these are used to evaluate the Maxwell field operators in the proximity of a source in series of powers or the transition moment on iteration. Comparison is then made with the analogous fields computed in the minimal-coupling scheme. Formulae are also given for the Fields of a Moving Source of charge. Two observables of the electromagnetic Field associated with a stationary distribution of charge, namely the Poynting vector and the energy density, are then calculated. The Source fields are then used in a response theory formalism to calculate the resonant transfer of energy between an excited and an unexcited pair Of Molecules, and the retarded van der Waals dispersion energy shift between two excited electric dipole polarizable molecules, from which the results when one or both of the pair is in the ground electronic state, are easily derivable. Extension of response theory to many-body dispersion forces is then Outlined, with explicit results being given for the retarded correction to the Axilrod-Teller-Muto three-body interaction energy.