Quantum Electrodynamics in Terms of Electromagnetic Field Intensities

John Dirk Walecka

Andreas Osterloh

Spin-boson interactions are at the heart of modern physics since they bridge the world of photons as described by quantum electrodynamics and that of quantum mechanics of massive objects, like atoms or ions. It is theoretically well understood that for an electric field which is polarized in e.g. x-direction, the electromagnetic dipole interaction produces a term , where is the electric field vector, is the position vector of an electron in the atom, a and are annihilation and creation operators of the electromagnetic field, respectively, and is the Pauli matrix in x-direction, in standard representation . Now, in highly intense light fields far off resonance (), as used in recent experiments, or where the underlying physics itself provides

Edwin Albert Power, T. Thirunamachandran

The electromagnetic field operators in the Heisenberg picture are found in both the minimal and multipolar forms of nonrelativistic quantum electrodynamics within the electric dipole approximation. These are made up of free- and source-field terms. The free electric- and magnetic-field operators in the two formalisms differ since the creation/annihilation operators are manifestly distinct. Their explicit forms in the Heisenberg picture are given. However, the source fields are formally the same when expressed in terms of dipole moment operators at positive retarded time. The cancellations that lead to this equivalence are presented. In many applications it is necessary to express the operators at retarded time in terms of creation and annihilation operators at the initial time. Explicit expressions for the fields up to second order in terms of the transition dipole moments are given. These enable the formulas for induced dipole moments to be derived within the context of quantum electrodynamics whereas previous derivations have been based on semiclassical electrodynamics.

O. B. Prepelitsa

Quantum-electrodynamic processes that take place in the presence of a squeezed electromagnetic field are discussed. Integral formulas are derived that make it possible to express the probability of any process in a squeezed electromagnetic field in terms of the probability of the same process in a classical electromagnetic field. The main laws that govern processes of first order in the fine-structure constant as functions of the number of photons involved and the quantum fluctuations are examined. Tunneling formulas for the probability of a photon producing an electron-positron pair in a strong squeezed field are derived. Also, resonant electron-electron scattering is examined and the scattering cross section as a function of the statistical properties of the field (the way the field has been squeezed) is investigated. It is found that the quantum fluctuations of the squeezed electromagnetic field give rise to an increase in the scattering cross section, with the probability of the process in a phase-squeezed electromagnetic field always being higher than the probability of the process in an amplitude-squeezed electromagnetic field.