Functional integral of QED in terms of gauge-invariant quantities

We reduce the functional integral of quantum electrodynamics to an integral containing only local gauge invariant quantities. The set of (bosonic) invariants contains bilinear combinations of the spinor field and a real-valued covector field.     

On background gauge-invariant regulators

Background gauge invariant regulators are studied. It is found that BRS invariance is needed only for the proper treatment of subdivergences. Gauge-invariant Pauli-Villars regularization is used as an example of such a regulator.     

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, α, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in α. In this sense, the dipole approximation is rigorously justified.     

Construction of a gauge-invariant cutoff of quantum electrodynamics from a non-local gauge-invariant Lagrangian

A non-local gauge-invariant Lagrangian is given, which describes gauge-invariant quantum electro-dynamics with a modified fermion propagator. Some examples are discussed.     

On the QED approach to frequency shifts

We comment on and correct recent works which 1) discuss the effect of the rotating wave app of radiative frequency shifts and 2) calculate level and frequency shifts by dispersion relations.     

Spinor electrodynamics in terms of gauge-invariant quantities

We give a formulation of classical spinor electrodynamics in terms of gauge-invariant quantities. The set of invariants consists of bilinear combinations of spinor fields (currents), a real-valued covector field, and a complex scalar field of modulus one. The presented result is a first step towards formulating quantum electrodynamics in terms of gauge-invariant fields.     

On the classical dynamics of charges in non-commutative QED

Following Wongs approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space.Received: 29 October 2003, Revised: 21 April 2004, Published online: 15 June 2004A.H. Fatollahi: Address after March 2004: Department of Physics, Alzahra University, Tehran, 19938-91167, Iran     

Torsion and gauge-invariant massive electrodynamics

We study electrodynamics in Einstein-Cartan space-time, that is, in space-time with torsion, and show an analogy with the Chern-Simons gauge-invariant massive electrodynamics. In our case, however, there is no arbitrary parameter, the torsionQ playing the role of the Chern-Simons parameter. This leads to bounds on the photon mass, charge, and torsion coupling.     

Locally gauge-invariant formulation of parastatistics

A locally gauge-invariant formulation of parastatistics, which is equivalent to a Yang-Mills gauge theory, is given, using a complex Clifford algebra (case of SU(N)) or a real Clifford algebra (case of SO(N)). In particular, for the SU(3) case, the gauged theory of para-Fermi quarks is equivalent to quantum chromodynamics.     

Renormalons in QED

Four-dimensional Quantum Electrodynamics is studied in the limit of a large number of leptons (N→∞) up to terms of order 1/N inclusive. It is proven that closed analytic expressions can be given for the Borel transform of Green's functions. Furthermore, an appropriate renormalization scheme is introduced. In this scheme, up to first order in the 1/N expansion, all the renormalization group functions are polynomials. Since renormalon singularities are explicitly known, the Borel summability of QED is discussed.     

On the dynamical mass generation in gauge-invariant non-linear σ-models

We argue that external gauge fields coupled in a gauge-invariant way to both the bosonic and supersymmetric two-dimensional non-linear σ-models acquire a dynamical mass term whenever the target space is restricted to be a group manifold.     

On the Absence of Excited Eigenstates of Atoms in QED

For the standard model of QED with static nuclei, nonrelativistic electrons and an ultraviolet cutoff, a new simple proof of absence of excited eigenstates with energies above the groundstate energy and below the ionization threshold of an atom is presented. Our proof is based on a multi-scale virial argument and exploits the fact that, in perturbation theory, excited atomic states decay by emission of one or two photons. Our arguments do not require an infrared cutoff (or regularization) and are applicable for all energies above the groundstate energy, except in a small (α-dependent) interval around the ionization threshold. also at IHES, Bures-sur-Yvette.     

Quark confinement and vortices in massive gauge-invariant QCD

Massive gauge-invariant QCD can support vortices (analogous to Nielsen-Olesen strings) of nearly finite classical action per unit area (there is a logarithmic short-distance singularity which is of little consequence). These vortices lead, in analogy to Abelian lattice-gauge theories, to confinement of fractionally charged quarks and color screening for gluons. In this paper, we make some qualitative remarks about the (Minkowski-space) dynamics which follows from this sort of confinement, studying not only $\text{q}\text{q}$ processes but also qqq processes. For the latter, the effective long-range vortex-induced interaction is approximately described as a sum of two-body potentials each of half the strength of the $\text{q}\text{q}$ potential (just as for the asymptotically free short-distance potentials), and linearly rising non-relativistically. There is an essential two-dimensionality about the confinement process which suppresses what would be the transverse degrees of freedom of strings joining quarks. A fully relativistic dynamics is given which is amenable to a simple phenomenological joining of long- and short-distance effects, with a running coupling constant such that g²(k) ～ k^?2 for small k. Spin-dependent potentials have no linearly-rising parts, and there are no strong Van der Waals forces. Little is said about gluon dynamics, except to point out the existence of rather massive hadronic glueballs and of (classically singular) instanton-like solutions which are screened at large distances.     

A manifestly gauge-invariant formulation of quantum electrodynamics

A manifestly gauge-invariant formulation of quantum electrodynamics is constructed in which the basic dynamical variables are physically observable quantities. The theory is relativistically covariant, because the structure of the Poincaré group is built into it from the beginning.     

On the Light-Cone Expansion in Gauge Field Theories (QED)

The techniques for the derivation of light-cone expansions in scalar field theories are generalized to nonscalar, especially gauge field theories. For this reason the smallness of the remainder is proved in an arbitrary renormalizable theory provided an infrared regularization is present. Then we apply the formalism to derive a light-cone expansion for the product of two scalar currents in Quantum Electrodynamics in leading order. Thereby the gauge-invariance of the underlying theory is used from the very beginning by the application of the known solutions of the Ward identities. As a result of that, one obtains two gauge-invariant light cone operators, and the corresponding coefficient functions are independent one from another.