洛伦兹破缺的电动力学模型

由于宇宙常数的存在, 时空为渐近de Sitter(dS)的时空. 文中将静态dS度规作为时空的近似刻画, 研究了在此度规下的一个洛伦兹破缺的电动力学模型. 通过张量的标架场分解的方法, 得到了静态dS时空中的电磁场方程. 另外, 分别研究了静态dS时空中点电荷的静电场和圈电流的静磁场, 并且同时讨论了在此模型下的洛伦兹破缺效应.     

Electrostatic and magnetostatic solutions in a Lorentz-violating electrodynamics model

We propose an effective Lorentz-violating electrodynamics model via the static de Sitter metric, which is deviated from the Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we derive the solutions of the electrostatic field and the magnetostatic field due to a point charge and a circle current, respectively, and discuss the implication of the effect of Lorentz violation in our electromagnetic theory.PACS 04.20.Cv; 04.40.-b; 98.80.Jk; 11.30.Cp     

On the effective lagrangian in spinor electrodynamics with added violation of Lorentz and <Emphasis Type="Italic">CPT</Emphasis>-symmetries

We consider quantum electrodynamics with additional coupling of spinor fields to the space-time independent axial vector violating both Lorentz and CPT-symmetries. The Fock-Schwinger proper-time method is used to calculate the one-loop effective action up to the second order in the axial vector and to all orders in the space-time independent electromagnetic field strength. We find that the Chern-Simons term is not radiatively induced and that the effective action is CPT-invariant in the given approximation. Received: 29 January 2003 / Published online: 24 March 2003 RID="a" ID="a" e-mail: sitenko@itp.unibe.ch RID="b" ID="b" e-mail: rulik@to.infn.it     

On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background

We show for the first time that the induced parity-even Lorentz invariance violation can be unambiguously calculated in the physically justified and minimally broken, dimensional regularization scheme, suitably tailored for a spontaneous Lorentz symmetry breaking in a field theory model. The quantization of the Lorentz invariance violating quantum electrodynamics is critically examined and shown to be consistent either for a light-like cosmic anisotropy axial-vector or for a time-like one, when in the presence of a bare photon mass.     

电磁场的复矢量表示

在麦克斯韦方程组及洛伦兹力密度公式基础上引入电磁场复矢量,讨论了电磁场普遍规律的新公式,包括对复矢量电磁场的建立,电荷守恒定律,能量守恒定律,电磁场矢势与标势,电磁场动量、能量、张量、相对论协变性等的研究,并和电动力学相比较,得出一些结论.     

Born-Infeld电动力学的U1主丛表述

本文给出了Born-Infeld电动力学的U₁主丛表述,以及检验粒子在Born-Infeld电磁场中的运动方程,检验粒子受到两个力,一个相当于Lorentz力,一个相当于Poincaré压力。     

Born-Infeld电动力学的U1主丛表述

本文给出了Born-Infeld电动力学的U₁主丛表述,以及检验粒子在Born-Infeld电磁场中的运动方程,检验粒子受到两个力,一个相当于Lorentz力,一个相当于Poincaré压力。     

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.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

On the Non-Lorentz-Invariance of <Emphasis Type="SmallCaps">M.W. Evans’</Emphasis><Emphasis Type="Italic">O</Emphasis>(3)-Symmetry Law

In 1992 M.W. Evans proposed the O(3) symmetry of electromagnetic fields by adding a constant longitudinal magnetic field to the well-known transverse electric and magnetic fields of circularly polarized plane waves, such that certain cyclic relations of a so-called O(3) symmetry are fulfilled. Since then M.W. Evans has elevated this O(3) symmetry to the status of a new law of electromagnetics. As a law of physics must be invariant under admissible coordinate transforms, namely Lorentz transforms, in 2000 he published a proof of the Lorentz invariance of O(3) symmetry of electromagnetic fields. As will be shown below this proof is incorrect; more, after simple correction it will turn out here that the O(3) symmetry cannot be Lorentz invariant.     

The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.     

Effective dynamics of a classical point charge

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.     

Photon spin and Bose-Einstein statistics

It is shown that Maxwell’s equations for the electric and magnetic fields free of sources can be inferred from Dirac’s pair of first-order equations for a zero-mass, zero-charge particle. This result is interpreted as a Lorentz invariant form of the transverse nature of photonic propagation in which only two components of the spin-1 field exist in nature.Canonical quantization of Dirac’s equations leads to a time average of the electromagnetic energy in agreement with the standard result of quantum electrodynamics. It is shown that the spin-statistics theorem is not violated for canonical quantization of the Dirac field provided the mass of the particle is zero.     

On a generalization of the equations of electrodynamics

Both the field equations and the equations of motion of a charged particle in an electromagnetic field are generalized. The sense of the generalization consists in giving up the Lorentz condition on the field potentials. The basic conclusion is that, in addition to the charge and mass, the proper rotation of the particle (the spin) should belong to the characteristics of a particle in classical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 107–110, July, 1972.The author wishes to thank the participants of the Ivanov Inter-Institute Seminar on Mathematical and Theoretical Physics for discussion of the results of the present work.     

The analog of electric and magnetic fields in stationary gravitational systems

Newtonian and Machian aspects of the stationary gravitational field are brought into formal analogy with a stationary electromagnetic field. The electromagnetic vector potential equals (up to a factor) the timelike Killing vector field. The current density is given by the contraction of the Killing vector with the Ricci tensor. A coordinate-dependent split in electric and magnetic field vectors is given, and some results of classical electrodynamics are used to illustrate the analogy. In the linearized theory, the usual Maxwell equations are obtained. The analogy also holds from the point of view of particle motion. The geodesic equation is brought into a special form that exhibits an analog to the Lorentz force. Two examples (which have played an important role in the theoretical discovery of Machian effects) are considered.     

On the Effective Metric for an Electromagnetic Wave Propagating in the Field of an Intense Laser Radiation

It is shown that in the nonlinear electrodynamics of vacuum, which is a corollary of quantum electrodynamics, a weak electromagnetic wave propagates in the field of an intense laser radiation as if this took place in some effective space-time whose metric tensor depends on the electric field of the laser radiation. The components of the metric vector of the effective space-time along the geodesic lines of which the rays of the weak electromagnetic wave propagate in the given case have been found. It is pointed out that this property may serve as a basis for observing the manifestations of the nonlinearity of the electrodynamics of vacuum.     

Electric strings and light-like lumps in classical electrodynamics

Soliton-like solutions of classical spinor electrodynamics with the symmetry of a cylinder of finite or infinite length are described. The solutions have non-vanishing total charge and, contrary to ordinary strings, an azimuthal magnetic and a radial electric field. For finite length, these lumps move with the velocity of light in the direction of the symmetry axis and the total four momentum is light-like. The crucial mechanism is a subtle compensation which prevents the matterfield from recoupling to its own electromagnetic field.     

Generally covariant nonlinear electrodynamics with a tensor potential

A generally covariant nonlinear electrodynamics with a tensor potential, constructed in analogy with Einstein's theory of gravitation, is proposed. It is shown that in weak electromagnetic fields (E, H < 10¹³ cgsoe units) the tensor electrodynamics passes over to the usual linear vector electrodynamics of Maxwell and Lorentz. The problem of the self-energy of a charge is solved in the framework of the proposed electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 98–102, October, 1972.For helpful discussions and important comments the author expresses thanks to Prof. D. D. Ivanenko and all participants in his seminar on the theory of the nucleus and elementary particles at the Moscow State University.     

Electromagnetic Field Theory Without Divergence Problems 1. The Born Legacy

Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell–Born–Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton–Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell–Born–Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.     

The vacuum-vacuum amplitude and Bogoliubov coefficients

We consider the problem of fixing the phases of Bogoliubov coefficients in quantum electrodynamics such that the vacuum-vacuum amplitude can be expressed via them. For a constant electric field and particles with spins of 0 and 1/2, this is done starting from the definition of these coefficients. Using the symmetry etween electric and magnetic fields, we extend the result to a constant electromagnetic field. It turns out that for a constant magnetic field, it is necessary to distinguish the in-and out-states, although they differ only by a phase factor. For a spin-1 particle with a gyromagnetic of ratio g=2, this approach fails and we reconsider the problem using the proper-time method.