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.     

Covariant calculation of effective cross sections in quantum electrodynamics. I

A special representation of the amplitudes of the electron and positron wave functions is used to derive a method for calculating the S-matrix elements. This method is analogous to that proposed in a previous paper by the author, but it gives equations in covariant notation.     

New space-time symmetries in the electrodynamics of a medium

New space-time symmetries are found in the electrodynamics of inertially moving media which are isotropic in the rest frame. It is shown that they can be uniquely described by a local Lorentz group with matrix-valued parameters. An algebra of first-order differential operators for this group is defined.Translated from Izvestiya Vysshikh Uchebnykh Zaivedenii Fizikg, No. 10, pp. 26–30, October, 1986.We wish to thank the participants of the theory seminar in the Physics Department of Minsk State University who took part in the discussion of this work~     

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 decomposition and polarizational selection rules for interaction among photons in a moving medium

Starting from the first principles we establish the symmetries under inversions and obtain relativistic tensorial decompositions for multiphoton amplitudes in moving isotropic homogeneous media. Basing on these decompositions we find universal selection rules with respect to polarizations for the processes of photon splitting and junction in a medium, as well as for photon-photon application to nonlinear wave processes.     

The supersingleton II: Composite electrodynamics

A formulation of composite electrodynamics, with scalar singleton constituents, is here extended to a supersymmetric theory of composite photons and neutrinos, in which the (massless) neutrinos are composed of one each of the scalar and spinorial singletons. These particles interact with an arbitrary scalar matter superfield, with massive, charged components. The feasibility of an interaction that is gauge invariant (in the sense of singleton gauge invariance) arises from the use of unconventional quantization rules which, in turn, are available because singletons are kinematically confined.     

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.     

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.     

Toward a nonlinear electrodynamics

An infinite series of Lorentz- and Poincare-invariant nonlinear versions of Maxwell's equations and nonhomogeneous d'Alambert's equations is proposed. Certain properties of these equations are examined.Kurchatovskii Institute Russian NTs. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 116–119, February, 1995.     

Covariant,algebraic, and operator spinors

We deal with three different definitions for spinors: (I) thecovariant definition, where a particular kind ofcovariant spinor (c-spinor) is a set of complex variables defined by its transformations under a particular spin group; (II) theideal definition, where a particular kind of algebraic spinor (e-spinor) is defined as an element of a lateral ideal defined by the idempotente in an appropriated real Clifford algebra _p,q (whene is primitive we writea-spinor instead ofe-spinor); (III) the operator definition where a particular kind of operator spinor (o-spinor) is a Clifford number in an appropriate Clifford algebra _p,q determining a set of tensors by bilinear mappings. By introducing the concept of spinorial metric in the space of minimal ideals ofa-spinors, we prove that forp+q5 there exists an equivalence from the group-theoretic point of view among covariant and algebraic spinors. We also study in which senseo-spinors are equivalent toc-spinors. Our approach contain the following important physical cases: Pauli, Dirac, Majorana, dotted, and undotted two-component spinors (Weyl spinors). Moreover, the explicit representation of thesec-spinors asa-spinors permits us to obtain a new approach for the spinor structure of space-time and to represent Dirac and Maxwell equations in the Clifford and spin-Clifford bundles over space-time.     

WKB-type expansion for Langevin equations: II. Covariant expansion

We show how to compute in a covariant way the WKB-type expansion for the transition probability density of the Markovian processes generated by general multiplicative noise Langevin equations. The method uses phase space functional integrals and normal coordinates around the classical path. We compare with our earlier non-covariant methods and compute explicitly the first order correction to the WKB-approximation.     

Covariant representations in a fibre bundle framework

Canonical and covariant representations of Lie groups of the semidirect product form G = N⊙K with N Abelian, are analyzed in a fibre bundle framework. We exhibit first the relationship between both kinds of representations in such framework. Two complementary methods of selecting irreducible representations from the covariant ones are developed. The first one proceeds by restriction to an invariant subspace and is exemplified in the case of massive integer spin representations of the Poincaré group. The second method takes quotients and is particularly useful when we deal with reducible but indecomposable representations. A family of stepped gauge transformations is generated when the method is used to obtain the covariant massless integer helicity representations of the Poincaré group; the electromagnetic and gravitational gauge transformations are just the first two cases of such a family.     

Consistent,Covariant and Multiplicative Anomalies

It is shown that the multiplicative anomaly in the vector-axial-vector model, which apparently has nothing to do with the breaking of classical current symmetries, nevertheless is strictly related to the well known consistent and covariant anomalies.     

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.     

Dirac Oscillator in a Galilean Covariant Non-commutative Space

We study the Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a ‘Galilean covariant’ approach, which consists in projecting the covariant equations from a (4,1)-dimensional manifold with light-cone coordinates, to a (3,1)-dimensional Galilean space-time. We obtain the exact wave functions and their energy levels for the plane and discuss the effects of non-commutativity.