Green’s functions for certain cases in nonlinear electrodynamics

Equations are proposed for handling inverse treatment and also to construct a nonlinear medium or choose a laser beam in order to obtain a field with the required characteristics. Atmospheric Optics Institute, Siberian Division, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 64–70, February, 1998.     

Euclidean Green functions for quantum Fainberg-Iofa fields

We give necessary and sufficient conditions for Euclidean Green functions to have analytic continuation to a relativistic field theory with exponential growth in momentum space (= the Fainberg-Iofa fields or the fields with fundamental length).     

Spectral ansatz in quantum electrodynamics: Spectral functions and gauge transformations

Using the ansatz of Delbourgo and Salam for the vertex function in quantum electrodynamics, we find approximations to the spectral functions of the electron propagator for covariant gauges. The consistency with the integral relations for the change of the exact spectral functions under covariant gauge transformations is investigated. The approximated spectral functions appear not to be gauge covariant in general.     

On the infrared singularities of Green's functions in quantum electrodynamics

We present a formal calculation of the infrared singularity structure of the fermion propagator in QED based on the Faddeev-Kulish asymptotic solution. The Renormalization program is reviewed in the context of the BPHZ subtraction scheme and a refinement of the Renormalization group methods is employed to study the infrared singularities in perturbation theory.     

Green functions for photovoltaic response of quantum wire-dot-wire junctions

We investigate the photovoltaic properties of a quantum dot connected to quantum wire reservoirs using numerical calculations within the non-equilibrium Green function formalism. We examine impacts of the hopping parameter that controls each dot-wire contact for a monochromatic light at energy equal to the isolated dot gap. Global current increases when the hopping decreases, following the short-circuit current and the open-circuit voltage.     

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.     

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.     

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.     

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.     

A renormalization prescription for massless quantum electrodynamics

An alternative proof of the Ward-Takahashi identity for perturbative quantum electrodynamics is given which makes no use of a gauge invariant regularization such as the Pauli-Villars loop subtraction or dimensional regularization. Instead, it is shown, in the presence of an arbitrary high momentum cutoff, that the exact W-T identity holds with an error ofO(1) with 0<<1. The proof involves a perturbative analysis of the Euclidean functional integral for QED by the tree expansion method.Research supported by the Natural Sciences and Engineering Research Council     

Nonsecular expansion for the evolution operator in nonrelativistic quantum electrodynamics

A solution is obtained for the evolution operator which describes a resonance interaction of a multilevel system with quantized electromagnetic field. Its Taylor expansion in the interaction parameter contains no secular terms. As an example, the interaction of a two-level system with one-mode field is considered (with one-and two-photon resonance).     

The thermal Green functions in nonextensive quantum statistical mechanics

The thermal Green functions of the quantum-mechanical harmonic oscillator are constructed within the framework of nonextensive statistical mechanics with normalized q -expectation values. For the Tsallis index q greater than unity, these functions are found to be expressed analytically in terms of the Hurwitz zeta function. It is found that influence of the nonextensivity on the time-ordered thermal propagator is relevant only at the “on-shell” states. In particular, the finite-temperature contribution to the thermal propagator becomes enhanced for the strong nonextensivity. Received 30 September 1998