Duality transformations for general abelian systems

We describe the general structure of duality transformations for a very broad set of abelian statistical and field theoretic systems. This includes theories with many different types of fields and a large variety of kinds of interactions including, but not limited to nearest neighbor, next nearest neighbor, multi-spin interactions, etc. We find that the dual form of a theory does not depend directly on the dimensionality of the theory, but rather on the number of fields and number of different kinds of interactions. The dual forms we find have a generalized gauge symmetry and possess the usual property of having a temperature (or coupling constant) which is inverted from that of the original theory. Our results reduce to the well-known results in those particular cases that have heretofore been studied. Our procedure also suggests variations capable of generating other forms of the dual theory which may be useful in various specific cases.     

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.     

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.     

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.     

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.     

First quantized electrodynamics

The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe–Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED.     

Testing Born-Infeld electrodynamics in waveguides

Waveguides can be employed to test nonlinear effects in electrodynamics. We solve Born-Infeld equations for TE waves in a rectangular waveguide. We show that the energy velocity acquires a dependence on the amplitude, and harmonic components appear as a consequence of the nonlinear behavior.     

A covariant method in electrodynamics

The tetrad formalism of Newman and Penrose is used to develop a method for solving Hamilton-Jacobi and Dirac equations and to calculate the intensity of radiation from a moving charged particle in external electromagnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 70–76, January, 1978.     

Axion electrodynamics in a waveguide

The interaction of axion and electromagnetic waves is studied in the presence of a magnetic field threading a waveguide. This interaction, which vanishes in free space, is found to induce transverse magnetic waves with frequency spectra associated with transverse electric waves in the absence of the axion.     

Dimensions and units in electrodynamics

We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwells equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call premetric classical electrodynamics. This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of L.B. Okun which he had presented at a recent conference.     

Light-light scattering in vector electrodynamics

Expressions for scattering amplitudes with definite polarizations in the approximation ω² ? m² are found. The asymptotic γγ→γγ total cross section is evaluated for the scattering of unpolarized photons. Also the forward scattering amplitudes and the differential cross section for forward scattering are obtained.     

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.     

Duality

Starting from the study of the physical world, we develop the concept of a dual pair, Comparing dual pairs is known as duality. We show that duality is a basic mechanism for our intellectual curiosity.     

Zero-point fluctuations in direct-action electrodynamics

In quantized direct interparticle Wheeler-Feynman electrodynamics, no free-field bosonic commutation relations exist. It is shown that a test atom will nevertheless detect a zero-point fluctuating “field” whose source is the atoms of the absorber.     

Time asymmetry in classical electrodynamics

Source-free Maxwell equations are recast in a form that incorporates manifest time reversal invariance. It is argued that potentials are fundamental quantities. The basis of a formulation in which the source and fields are unified is also outlined.     

Wave propagation in axion electrodynamics

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern–Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor. We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian.     

Local nonlinear electrodynamics

The propagation of electromagnetic waves in dielectric media characterized by the coefficients and is examined in the eikonal approximation of electrodynamics. Employing the techniques Hadamard-Papapetrou (HPD) and Spacetime Integration (STI), we derive the dispersion relation, the polarization modes and effective geometry associated to the model.     

Octonion massive electrodynamics

In this paper, we have made an attempt to reformulate the generalized field equation and various quantum equations of massive dyons in terms of octonion eight dimensional space as the combination of two (external and internal) four dimensional spaces. The octonion forms of generalized potential and current equations of massive dyons are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion massive electrodynamics in manifestly covariant and consistent manner.