Construction of two-dimensional quantum electrodynamics based on a Hamiltonian formalism

After completing the renormalization of the Hamiltonian of (QED)₂ based on an indefinite metric formalism of the vector field, its diagonalization and the properties of the physical vacuum are investigated.     

Quantum gravitational contributions to the beta function of quantum electrodynamics

We show in a diagrammatic and regularization independent analysis that the quadratic contribution to the beta function which has been conjectured to render quantum electrodynamics asymptotically free near the Planck scale has its origin in a surface term. Such surface term is intrinsically arbitrarily valued and it is argued to vanish in a consistent treatment of the model.     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Reggeization of the photon in quantum electrodynamics

Under certain assumptions it is shown that in massless QED the photon may reggeize. Our technique involves a comparison of the infrared spectrum with that of the di-triple Regge expansion of inclusive processes.     

Infrared problems in quantum electrodynamics

We present a self-contained treatment of the infrared problem in Quantum Electrodynamics. Our program includes a derivation and proof of finiteness of modified reduction formulae for scattering in Coulomb potentials and unitary extensions of the relativistic Coulomb amplitudes in the forward direction. The renormalization structure of the theory is discussed in connection with the infrared problem and the renormalization group is reconsidered and shown to be inadequate for the “improvement” of perturbation theoretic results. However, simple forms of the renormalization group equations are easily established, which allow for a simple discussion of the renormalization structure and the extraction of physical quantities out of Green functions normalized at an arbitrary mass μ < m (m is the fermion mass). As an example of such a quantity we consider the construction of a renormalized and infrared finite mass-operator in presence of external fields. Scattering theory in Quantum Electrodynamics is elaborated in the context of the coherent state formulation of the asymptotic condition. Dimensional regularization techniques are systematically used for the reduction of coherent states and the construction of S-matrix elements and the cross-section formulae. The latter are obtained in a relatively simple form, which allows for a direct comparison with the exact cross-section formulae derived in the traditional context. This establishes the equivalence of the two approaches at the cross-section level. Various applications illustrate the techniques presented here and relative topics are discussed.     

Critical charge in quantum electrodynamics

The critical nuclear charge Z _cr and the critical distance R _cr in the system of two colliding heavy nuclei—they are defined as those at which the ground-state level of the electron spectrum descends to the boundary of the lower continuum, with the result that beyond them (that is, for Z>Z _cr or R<R _cr) spontaneous positron production from a vacuum becomes possible—are important parameters in the quantum electrodynamics of ultrastrong Coulomb fields. Various methods for calculating Z _cr and R _cr are considered, along with the dependence of these quantities on the screening of the Coulomb field of a nucleus by the electron shell of the atom, on an external magnetic field, on the particle mass and spin, and on some other parameters of relevance. The effective-potential method for the Dirac equation and the application of the Wentzel-Kramers-Brillouin method to the Coulomb field for Z>137 and to the two-body Salpeter equation for the quark-antiquark system are discussed. Some technical details in the procedure for calculating the critical distance R _cr in the relativistic problem of two Coulomb centers are described.     

The quantum electrodynamics of the nucleon

The Nuclear Force between a statistical assemblage of nucleon pairs is calculated directly for pseudo-scalar meson exchange. The Nucleon (proton) is treated as a particle with an extended structure. The model of the proton used is the one determined by high energy electron-proton scattering experiments.The self-energy process for such a proton is examined first for the emission and re-absorption of a photon. An appropriate photon propagator is derived for such a system using variational techniques. It is shown that the integrals that occur in the self-energy process converge without any of the difficulties associated with the point charge model. This shows the divergences in Quantum Electrodynamics (for nucleons) do not exist when nucleons are treated as particles with a structure.The pseudo-scalar meson propagator is derived using similar methods and the exchange force is calculated. It is shown that only certain diagrams need be considered when a stable nuclear bond is being calculated. The corrections to the Nuclear Force, which are self-energy processes involving emission and re-absorption of Virtual pseudoscalar mesons, are shown to converge for strong coupling.     

Vacuum behavior in two-dimensional scalar electrodynamics

The vacuum properties in two-dimensional scalar electrodynamics are investigated by calculating the one-loop contribution to the effective lagrangian for a constant electric field.     

On the subsidiary condition in quantum electrodynamics

It is proven that no charged state obtained by applying a local operator to the vacuum can satisfy the Gupta-Bleuler subsidiary condition. The meaning of this result is illustrated in the simple model whereby the vector potential is coupled to an external classical current. Alternative ways of handling the difficulty with the subsidiary condition are listed.     

Differential representation of the delta function in two-dimensional quantum mechanics

The exactly solvable model of a two-dimensional system consisting of a particle in a Dirac delta function potential is studied in position space in lieu of momentum space. This study is facilitated by representing the delta function as the second derivative of a radial function, which depends on a length scale. Such a representation of the delta function provides an instructive approach to understanding the role of an arbitrary length scale in the concepts of regularization and renormalization.     

Theoretical analysis of quantum electrodynamics

A study is carried out of some of the important developments made in quantum electrodynamics (QED) during this past decade. Basic problems and recent attempts are considered which are expected to be of importance not only for further developments in QED, but also to our further understanding of quantum field theory, in general and of its unique role played in describing the dynamics of elementary particles.