Successive Lorentz transformations of the electromagnetic field

A velocity-orientation formalism to deal with compositions of successive Lorentz transformations, emphasizing analogies shared by Lorentz and Galilean transformations, has recently been developed. The emphasis in the present article is on the convenience of using the velocity-orientation formalism by resolving a paradox in the study of successive Lorentz transformations of the electromagnetic field that was recently raised by Mocanu. The paradox encountered by Mocanu results from the omission of the Thomas rotation (or, precession) which is involved in the composition of two Lorentz transformations with corresponding noncollinear velocity parameters. By resolving this paradox, we expose (i) the central role that the Thomas rotation plays in special relativity, (ii) the need to consider in special relativity orientations in addition to velocities between inertial frames, and (iii) the power and elegance of the novel velocity-orientation formalism. A similar paradox in STR that Mocanu pointed out, also resulting from the omission of the Thomas rotation, has been resolved in a previous communication.     

Electron in crossed constant electromagnetic fields and a plane wave field

The Dirac equation for an electron interacting with constant homogeneous orthogonal magnetic and electric fields (E = H) and with the field of a plane wave being propagated in a direction perpendicular sto E and H is solved exactly. The plane wave field is hence considered either classically or in a quantized manner, or as the field of a wave consisting of classical and quantized parts.     

Exact solutions of the Loretnz-Dirac equations of motion for charged particles in constant electromagnetic fields

The linearized Lorentz-Dirac equation $\text{u}\text{?}{}^{\mathrm{\mu }}\text{= F}{}^{\mathrm{\mu \nu }}\text{u}{}_{\mathrm{\nu }}\text{- κ(F}{}^{\mathrm{\mu \sigma }}\text{F}{}_{\mathrm{\lambda \sigma }}\text{u}{}^{\mathrm{\lambda }}\text{+ {F}{}^{\mathrm{\sigma \mu }}\text{u}{}_{\mathrm{\nu }}\text{F}{}_{\mathrm{\sigma \lambda }}\text{u}{}^{\mathrm{\lambda }}\text{}u}{}^{\mathrm{\mu }}\text{)}$ is solved in closed form for arbitrary constant electromagnetic fields. These solutions are also a convenient starting point to treat particle motion in the slowly varying electromagnetic fields surrounding a pulsar in the near field zone.     

Green's functions of linear and three dimensional oscillators in a constant and homogeneous electromagnetic field

The retarded Green's functions are found for linear and three dimensional harmonic oscillators in constant and uniform electric and magnetic fields. These results are applied to the problem of the motion of wave packets of Gaussian shape.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 29–33, August, 1973.In conclusion the authors thank A. A. Sokolov for a discussion of the obtained results.     

Vector boson in the constant electromagnetic field

The propagator and the complete sets of in-and out-solutions of the wave equation, together with the Bogoliubov coefficients relating these solutions are obtained for the vector W-boson (with the gyromagnetic ratio g=2) in a constant electromagnetic field. When only the electric field is present, the Bogoliubov coefficients are independent of the boson polarization and are the same as for the scalar boson. For the collinear electric and magnetic fields, the Bogoliubov coefficients for states with the boson spin perpendicular to the field are again the same as in the scalar case. For the W ^? spin parallel (antiparallel) to the magnetic field, the Bogoliubov coefficients and the one-loop contributions to the imaginary part of the Lagrange function are obtained from the corresponding expressions for the scalar case by the substitution m ² → m ²+2eH (m ² → m ²-2eH). For the gyromagnetic ratio g=2, the vector boson interaction with the constant electromagnetic field is described by the functions that can be expected by comparing the scalar and Dirac particle wave functions in the constant electromagnetic field.     

QED effective action in a constant electromagnetic field under conditions of possible Lorentz invariance violation in the Dirac equation

This paper is devoted to the calculation of corrections to QED effective action associated with the axial-vector condensate b ^μ, which violate the Lorentz invariance. It was shown that the linear in b ^μ contribution to the 1-loop effective action (Chern-Simons term) is absent in the case of a constant electromagnetic field. The contribution, which is quadratic in b ^μ, was calculated for the cases of both constant magnetic and electric fields. Asymptotic estimates of the quadratic in b ^μ term for strong and weak field strengths were obtained.     

The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of “spacelike linearity”. Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.     

Spatial correlations and degree of polarization in homogeneous electromagnetic fields

We consider stationary electromagnetic fields modeled as superpositions of unpolarized and angularly uncorrelated plane waves and show that in anisotropic case the electric cross-spectral tensor is proportional to the imaginary part of the Green tensor. This is as for blackbody radiation, but here the field need not be in thermal equilibrium. We also evaluate the degree of polarization for a homogeneous but nonisotropic field for which the plane waves propagate within a cone of angles. The results are compared with the known polarization properties of blackbody radiation.     

Charged particle motion in superstrong electromagnetic fields

The motion of charged particles in superstrong electromagnetic fields studied analytically and numerically. An analytic solution is given for constant fields which also describes satisfactorily the initial part of the motion in the slowly varying fields surrounding a pulsar.     

Long-time behavior of the Lorentz electron gas in a constant,uniform electric field

The long-time behavior of the Lorentz electron gas is studied in the presence of a uniform external field. A discussion of the rigorous solution of the one-dimensional Boltzmann equation is followed by the derivation of the asymptotic form of the velocity distribution in an arbitrary number of dimensions. The system is shown to absorb energy from the field without bounds, which excludes the usually assumed steady state with finite thermal energy density.Supported by the Polish Ministry of Higher Education, Science and Technology, Project MR.I.7.The authors are very grateful to Dr. Y. Pomeau for many valuable comments.     

Maximum visibility under unitary transformations in two-pinhole interference for electromagnetic fields

In terms of the spectral density tensors associated with the electric field vector, the maximum visibility one can obtain in a two-point interference arrangement by using local (i.e., position-dependent) unitary transformations applied at such points is determined. It is also shown that the maximum visibility can be expressed in terms of a number of well-known parameters describing the coherence and polarization features of the field.     

Decomposition of transformations of inverse-radius vectors into a collection of transformations from the weyl group. The conformal dimension of the electromagnetic field

It is shown that transformations of the inverse radius-vectors are decomposable into four collections of transformations from the Weyl group. We consider the transformation properties and conformal dimensions of the fields, potentials, and the density of currents and charges of double-charge electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 9–13, May, 1990.     

Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.     

The singularity of homogeneous cosmological models with electromagnetic fields

The regime of approaching the singularity in the presence of electromagnetic fields has been found. The rotation angles of the Kasner axes are calculated.