scholarly journals Classical electrodynamics and gauge symmetry of the X-boson

2018 ◽  
Vol 33 (25) ◽  
pp. 1850148
Author(s):  
Mario J. Neves ◽  
Lucas Labre ◽  
L. S. Miranda ◽  
Everton M. C. Abreu
Keyword(s):  
Gauge Symmetry ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Massless Particle ◽  
Space Time ◽  
Dispersion Relations ◽  
Classical Electrodynamics ◽  
Gauge Transformations ◽  
Boson Model ◽  
A Charge

The classical electrodynamics for X-boson model is studied to understand it propagation in the space–time. The Maxwell equations of model and the correspondents wave equations are obtained. It indicate the dispersion relations of a massive and massless particle, that we interpret as photon and the X-boson. Thereby, a full diagonalization of the model is introduced to get a Maxwell sector summed up to Proca sector. Posteriorly, the X-fields and X-potentials of a relativistically moving charge is obtained in terms of a time-proper integral, and as an example, we calculate the fields and potentials for a charge in uniform moving. Finally, the gauge symmetry and gauge transformations were discussed.

scholarly journals AXION-ELECTROMAGNETIC WAVES

2013 ◽  
Vol 28 (35) ◽  
pp. 1350162 ◽  
Author(s):  
LUCA VISINELLI
Keyword(s):  
Gauge Symmetry ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Internal Symmetry ◽  
Classical Electrodynamics ◽  
Gauge Potential ◽  
Explicit Solutions ◽  
Duality Symmetry ◽  
Axion Field ◽  
External Sources

We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell equations that preserves this symmetry. This new set of equations allows for a gauge symmetry extending the ordinary symmetry in the classical electrodynamics. We obtain explicit solutions for the new set of equations in the absence of external sources, and we discuss the implications of a new internal symmetry between the axion field and the electromagnetic gauge potential.

A new approach on electromagnetism with dual number coefficient octonion algebra

2016 ◽  
Vol 13 (09) ◽  
pp. 1630013 ◽  
Author(s):  
Bhupesh Chandra Chanyal ◽  
Sunil Kumar Chanyal ◽  
Özcan Bektaş ◽  
Salim Yüce
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Space Time ◽  
Internal Space ◽  
Field Equations ◽  
Octonion Algebra ◽  
New Approach ◽  
Dual Number ◽  
Symmetrical Form ◽  
Unit Formula

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.

Linearized electromagnetic and gravito-Heavisidian chirality in split octonion space-time

2018 ◽  
Vol 15 (07) ◽  
pp. 1850109
Author(s):  
B. C. Chanyal
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Constitutive Relations ◽  
Electromagnetic Theory ◽  
Space Time ◽  
Alternative Form ◽  
Chiral Field ◽  
Chiral Media ◽  
First Approximation ◽  
Vector Matrix

In this paper, we construct a split octonionic mathematical approach to generalized electromagnetic and gravito-Heavisidian chirality of dyons by modification of the Drude–Born–Fedorov constitutive relations. In this context, we describe dual Euclidean space-times structure associated with [Formula: see text] Zorn’s vector matrix realization of split octonion. As such, using the Zorn’s vector matrix realization, an alternative form of generalized Proca–Maxwell equations of massive dyons is obtained in chiral media. It is well known that in weak unified gravito-Heavisidian field, the Einstein’s equations become Maxwell-like equations under the first approximation. Thus, we study the gravito-Heavisidian analogous theory to electromagnetic theory, and discuss the Drude–Born–Fedorov constitutive relations, gravito-Heavisidian field, Proca–Maxwell equations and gravito-Heavisidian wave equations for linear gravitational chiral field of gravito-dyons in flat split octonion space-time.

scholarly journals NECESSITY OF SIMULTANEOUS CO-EXISTENCE OF INSTANTANEOUS AND RETARDED INTERACTIONS IN CLASSICAL ELECTRODYNAMICS

1999 ◽  
Vol 14 (24) ◽  
pp. 3789-3798 ◽  
Author(s):  
ANDREW E. CHUBYKALO ◽  
STOYAN J. VLAEV
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Direct Interaction ◽  
Classical Electrodynamics ◽  
Constant Acceleration ◽  
Action At A Distance ◽  
A Charge ◽  
Accelerated Charge

We consider the electromagnetic field of a charge moving with a constant acceleration along an axis. We find that this field obtained from the Liénard–Wiechert potentials does not satisfy Maxwell equations if one considers exclusively a retarded interaction. We show that if and only if one takes into account both retarded interaction and direct interaction (so-called "instantaneous action at a distance") the field produced by an accelerated charge satisfies Maxwell equations.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Space-Time Coupling: Current Concept and Two Examples from Ultrafast Optics Studied Using Exact Solution of EM Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 529
Author(s):  
Nikolay L. Popov ◽  
Alexander V. Vinogradov
Keyword(s):  
Wave Equations ◽  
Coherent Control ◽  
Ultrafast Optics ◽  
Spectral Width ◽  
Space Time ◽  
Current Approach ◽  
Unipolar Pulse ◽  
Number Of Cycles ◽  
Control Of Quantum Systems ◽  
Coupling Current

Current approach to space-time coupling (STC) phenomena is given together with a complementary version of the STC concept that emphasizes the finiteness of the energy of the considered pulses. Manifestations of STC are discussed in the framework of the simplest exact localized solution of Maxwell’s equations, exhibiting a “collapsing shell”. It falls onto the center, continuously deforming, and then, having reached maximum compression, expands back without losing energy. Analytical solutions describing this process enable to fully characterize the field in space-time. It allowed to express energy density in the center of collapse in the terms of total pulse energy, frequency and spectral width in the far zone. The change of the pulse shape while travelling from one point to another is important for coherent control of quantum systems. We considered the excitation of a two-level system located in the center of the collapsing EM (electromagnetic) pulse. The result is again expressed through the parameters of the incident pulse. This study showed that as it propagates, a unipolar pulse can turn into a bipolar one, and in the case of measuring the excitation efficiency, we can judge which of these two pulses we are dealing with. The obtained results have no limitation on the number of cycles in a pulse. Our work confirms the productivity of using exact solutions of EM wave equations for describing the phenomena associated with STC effects. This is facilitated by rapid progress in the search for new types of such solutions.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

Sign in / Sign up

Export Citation Format

Share Document