Double-logarithmic nonlinear electrodynamics

Modern Physics Letters A, 2015

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also prove that there is only one analytic nonlinear electrodynamics not presenting birefringence.

Journal of Physics Communications, 2020

Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the electromagnetic vector potential is solved perturbatively about the known exact plane wave solution in both the case of a polarized vacuum without external field, as well as when a constant magnetic field is applied. A nonlinear wave equation with nonzero convective part for the (relatively) slowly varying amplitude of the first-order perturbation has been derived. This equation governs the propagation of electromagnetic waves with a reduced speed of light, where the reduction is roughly proportional to the intensity of the initial pumping plane wave. A system of coupled nonlinear wave equations for the two slowly varying amplitudes of the first-order perturbation, which describe the two polarization states, has been obtained for the case of constant magnetic ...

This paper presents an alternative to the Maxwell vacuum equations pre-relativistic approach to description of electromagnetic field objects. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature and the physical relations represented by them should represent local stress-energy-momentum balance relations. Such a view does not go along with the classical assumption for local recognizability of the electric and magnetic constituents E and B as time-stable and space propagationg subsystems of the field objects. The corresponding reconsideration brought us to the assumption, that the two couples (E, B) and (−B, E) are much more adequate in this respect: free electromagnetic field objects exist in a permanent propagation with the fundamental velocity c, so each of its recognizable subsystems should be able to carry momentum, and neither E nor B are able to do this separately, while each of the couples (E, B; −B, E) is able to do this, but only in presence of the other. Therefore, the necessary internal local dynamics, admissible changes, time stability and recognizability during space propagation should be viewed in terms of (E, B) and (−B, E) and their mutually compatible changes.

1997

This paper aims to consider the general properties of the non-linear solutions to the vacuum equations of Extended Electrodynamics. The *-invariance and the conformal invariance of the equations are mentioned. It is also proved that all non-linear solutions have zero invariants: F_{\mu\nu}F^{\mu\nu} = (*F)_{\mu\nu}F^{\mu\nu} = 0. The three invariant characteristics of the non-linear solutions: amplitude, phase and scale factor are introdiced and discussed.

2004

This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out in relativistic terms in Minkowski space-time. The non-linear vacuum solutions are considered and fully described. It is specially pointed out that solitary waves with various, in fact arbitrary, spatial structure and photon-like propagation properties exist. The {\it null} character of all non-linear vacuum solutions is established and extensively used further. Coordinate-free definitions are given to the important quantities {\it amplitude} and {\it phase}. The new quantity, named {\it scale factor}, is introduced and used as a criterion for availability of rotational component of propagation of some of the nonlinear, i.e. nonmaxwellian, vacuum solutions. The group structure properties of the nonlinear vacuum solutions are analyzed in some detail, showing explicitly the connection of the vacuum solutions with some complex valued functions. Connection-curvature interpretations are given and a special attention is paid to the curvature interpretation of the intrinsic rotational (spin) properties of some of the nonlinear solutions. Several approaches to coordinate-free local description and computation of the integral spin momentum are considered. Finally, a large family of nonvacuum spatial soliton-like solutions is explicitly written down, and a procedure to get (3+1) versions of the known (1+1) soliton solutions is obtained.

Eprint Arxiv Patt Sol 9711002, 1997

Eprint Arxiv Physics 0103061, 2001

The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work previously presented in [11], [12] and [13]. In particular, I display new types of both dynamic and static solutions of the Nonlinear Maxwell Equations (NM). I point out how the resulting theory ties to the Quantum Mechanics of Correlated Electrons inasmuch as it provides a mesoscopic description of phenomena like nonresistive charge transport, static magnetic flux tubes, and charge stripes in a way consistent with both the phenomenology and the microscopic principles. In addition, I point at a bunch of geometric structures intrinsic for the theory. On one hand, the presence of these structures indicates that the equations at hand can be used as 'probing tools' for purely geometric exploration of low-dimensional manifolds. On the other hand, global aspects of these structures are in my view prerequisite to incorporating (quantum) informational features of Correlated Electron Systems within the framework of the Nonlinear Maxwell Theory. * The author is currently with the Pegasus Imaging Corporation. This work is beyond the scope of his obligations there and has been performed in his free time. No other institution has been helpful to the author in conducting this research.

Physical Review D, 2013

Wave propagation in nonlinear theories of the electromagnetism described by Lagrangian densities dependent upon its two local invariants LðF; GÞ is revisited. On the light of the recent findings in metamaterials, it is here shown that trirefringence is also a possible phenomenon to occur in the realm of such nonlinear theories. A specific model exhibiting this effect is investigated in terms of both phase and group velocities. It is claimed that wave propagation in some well known nonlinear models for spin-one fields, like QED and QCD in certain regimes, may exhibit trirefringence.

Physical Review D

We consider the Plebański class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a theory, on an unspecified general-relativistic spacetime and with an unspecified electromagnetic background field. To that end we start out from an approximateplane-harmonic-wave ansatz that takes the generation of higher harmonics into account. By this ansatz, the electromagnetic field is written as an asymptotic series with respect to a parameter α, where the limit α → 0 corresponds to sending the frequency to infinity. We demonstrate that by solving the generalized Maxwell equations to zeroth and first order with respect to α one gets a unique transport law for the polarization plane along each light ray. We exemplify the general results with the Born-Infeld theory.

2003

The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born and Infeld are presented in the language of the modern geometrical and topological methods of mathematical physics. The manner by which spacetime curvature and topology can affect electromagnetism is also reviewed. Finally, the phenomena of nonlinear optics are reviewed as a possible guide to building one's intuition regarding the process of extending electrodynamics into nonlinearity in a manner that is consistent with the qualitative and empirical results of quantum electrodynamics.