Composite electrodynamics

This paper solidifies the foundations for a singleton theory of light, first proposed two years ago. This theory is based on a pure gauge coupling of the scalar singleton field to the electromagnetic current. Like quarks, singletons are essentially unobservable. The field operators are not local observables and therefore need not commute for spacelike separation. This opens up possibilities for generalized statistics, just as is the case for quarks. It then turns out that a pure gauge coupling, in which ∂μφ(x) couples to the conserved current j^μ(x), generates real interactions— the effective theory is precisely ordinary electrodynamics in de Sitter space. Here we improve our theory and explain it in much more detail than before, adding two new results. (1) The concept of normal ordering in a theory with unconventional statistics is worked out in detail. (2) We have discovered the natural way of including both photon helicities. Quantization, it may be noted, is a study in representation theory of certain infinite-dimensional, nilpotent Lie algebras, of which the Heisenberg algebra is the prototype.     

The supersingleton I: Free dipole and interactions at infinity

The program of this Letter, and the one following it, is to develop a formulation of supersymmetric electrodynamics in which the massless fields (photons and neutrinos) are bilinear (actually, commutators) of constituent singleton fields. here we lay the foundations, describing the unique gauge invariant interaction that is allowed in the context of conventional quantum field theory. New quantization rules, leading to super QED, are dealt with in the second Letter.     

Covariant electrodynamics in a medium,II

The energy-momentum and angular momentum emission rates for an arbitrarily moving charge (whose speed is less than that of light in the medium) in a uniform transparent medium are calculated in manifestly covariant form. The calculations are executed for three types of stress tensor: Minkowski, Abraham, and Marx. Among other things it is found that the energy-momentum emission rates for the latter two tensors are equal and differ from that of the former. Further, the angular momentum emission rates for all three tensors are found to be equal. Only for the Marx tensor is this rate independent of the orientation of the associated asymptotic space-like surface.     

On the electrodynamics of the type II superconductors

Using the two fluid model, modified Londons equations have been obtained for the type II superconductors in the Schubnikov state (H _c1<H<H _c2). The effect of the normal electrons which form the cores of the flux vortices have been included. These equations can be reduced to the Londons equations under suitable assumptions. The electric field inside the superconductor and the field equations have also been obtained.     

A new variant of nonlinear electrodynamics. II

The electrostatic solution of nonlinear electrodynamic equations is studied, the characteristic peculiarity of these equations being their consideration of the effect of electromagnetic spin on the space-time continuum. The energy of the nonlinear electromagnetic field proves to be finite for a quite wide spectrum of seed masses. Three-dimensional soliton solutions are constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 46–53, October, 1978.We express our deep indebtedness to N. N. Kolesnikov, V. R. Khalilov, and participants in the theoretical physics seminar led by Professor D. D. Ivanenko for evaluating the results of the study.     

Nonperturbative quantum electrodynamics: The Lamb shift

The nonlinear integro-differential equation, obtained from the coupled Maxwell-Dirac equations by eliminating the potential A, is solved by iteration rather than perturbation. The energy shift is complex, the imaginary part giving the spontaneous emission. Both self-energy and vacuum polarization terms are obtained. All results, including renormalization terms, are finite.     

Weber electrodynamics,part II unipolar induction,Z-antenna

Weber electrodynamics predicts the localized unipolar induction observed by Müller and Kennard; whereas the Maxwell theory, based upon closed current loops and the flux rule, fails. The Weber theory for high frequency fields predicts a zero self torque on the Pappas-Vaughan Z-antenna, as observed. In contrast, the Maxwell theory predicts a sizeable self torque which is not observed.     

Covariant calculation of effective cross sections in quantum electrodynamics. II

Equations are derived for expressing the exchange terms of an S-matrix element in terms of nonexchange terms. There is a discussion of a method for transforming from the matrix element to the effective cross section in which the cross section can be obtained in explicitly covariant form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 85–88, March, 1975.The authors thank A. B. Kukanov for interest in this study.     

The two-body multipole problem of electrodynamics

A 2-body system composed of two objects having arbitrary distributions of charge and current is discussed. An expression for the velocity dependent potential between these two objects has been obtained in the non-relativistic approximation. This potential consists of two parts viz. a velocity independent scalar potential Φ_eff and another part which is linearly dependent on the relative velocity between the objects. The second part naturally suggests a vector potential A_eff. The potentials have been expanded into multipole terms. It has been found that Φ_eff is a sum of two components viz. Φ_EE and Φ_MM such that each multipole term in Φ_EE represents an interaction between the electric multipoles of the two systems, each term in Φ_MM represents an interaction between their magnetic multipoles whereas each term in A_eff represents an interaction between an electric multipole of one and a magnetic multipole of the other. The results have been applied to the interaction between an electric dipole and a magnetic dipole. The symmetry among the multipole terms in A_eff suggests vanishing vector potential between two identical objects. A corollary of this appears to be absence of spin orbit interaction between two identical particles in the same spin state.     

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.     

The Lamb shift in finite electrodynamics

Using the finite-electrodynamics model, in which the electromagnetic field is considered as classical but the nature, classical or quantum, of the source of the field is unspecified, we establish, in a very simple way, a general formula associated with the self-energy of a time-periodic system of charges. By applying this formula to the currents associated with an electron bound in a hydrogen-like atom, one obtains immediately the Lamb shift standard formulas.     

On the well-posed two-body problem in electrodynamics and special relativity II

The initial segment problem for two interacting charged particles is studied and errors are corrected in the author's previous paper on this problem. An existence/uniqueness theorem hods for the forward extension under retarded interaction; a uniqueness theorem holds for the backward extension and also for time-symmetric interactions. An example is given which shows the difficulties which can arise in backwards extension.     

The natural line-breadth in stochastic electrodynamics

The fact that the formalism of stochastic electrodynamics includes the reaction force, makes the calculation of the natural line-breadth straightforward. The evaluation of the relativistic correction to energy levels is greatly simplified in stochastic electrodynamics and brings out the concept of the propagation of the Coulomb field with the velocity of electromagnetic waves.     

Semiclassical electrodynamics of alien atoms in interacting media II. Two-level systems

The previously developed self-consistent mean field theory of atoms entering an interacting medium is specialized to two-level alien atoms. It is shown that the medium may invert or split the original two levels, and that there is an intimate connection between the dressed atom spectrum and the statistical nature of the ensemble of alien atoms in the self-consistent mean field approximation. The optical susceptibility of alien atoms while inside the medium is calculated, and the lineshape and position of the optical resonance are shown to depend on the intensity of the optical field applied. There may be more than one phase possible for the atomic ensemble as a result of optical excitation.     

Beam-plasma electrodynamics

Charged-particle beams in dense plasmas are electrically self-focused for β² < $\text{1}\text{2}$ and magnetically self-focused for β² > $\text{1}\text{2}$. Rapidly varying intense cold beams in plasmas produce strong coherent electric oscillations due to the addition of Bohr-wake fields.     

p-Form electrodynamics

A generalization of gauge theory in which the gauge potential1-form is replaced by a p-form is studied. Charged particles are then replaced by elementary extended objects of dimension p–1. It is shown that this extension is compatible with space-time locality only if the gauge group is U(1). A source which is a closed p–1 surface has zero total charge and corresponds to a particle-antiparticle pair. Its quantum rate of production in an external uniform field is evaluated semiclassically. The analog of the Dirac magnetic pole is constructed. It is another extended object, of dimension n–p–3, where n is the dimension of space-time. The electric and magnetic charges obey the Dirac quantization condition. This condition is derived in two different ways. One method makes use of local gauge patches and the other brings in singular gauge transformations. A topological mass term is introduced and it is shown that it can coexist with a magnetic pole when n=2p+1, provided the topological mass is quantized.     

Self-energy quantum electrodynamics: Multipole radiation

Within the context of Barut's self-field approach to quantum electrodynamics, we show that the exact relativistic expression for the Einstein A-coefficient of atomic spontaneous emission reduces, in the long wavelength approximation, to a form containing electric- and magnetic-like multipole contributions related to the transition charge and current distributions of the relativistic electron. A number of interesting features of the expressions involved are discussed, and their generalization to interacting composite systems is also pointed out.Dedicated to Prof. A. O. Barut, teacher and friend, on the occasion of his 65th birthday. I only hope it measures up to the man being honored.