scholarly journals Electrodynamics in noninertial frames

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Maxwell Equations ◽  
Line Element ◽  
Minkowski Spacetime ◽  
Electromagnetic Theory ◽  
Coordinate Transformations ◽  
Biharmonic Equations ◽  
Classic Problem ◽  
Frame Systems ◽  
Generally Covariant ◽  
Arbitrary Charge

AbstractThe electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relativistic formulation of Maxwell’s electrodynamics arises in the flat Minkowski spacetime when the general coordinate transformations are restricted to a class of transformations preserving the Minkowski line element. The particular attention is paid to the analysis of the electromagnetism in the noninertial rotating reference system. For the latter case, the general stationary solution of the Maxwell equations in the absence of the electric current is constructed in terms of the two scalar functions satisfying the Poisson and the biharmonic equations with an arbitrary charge density as a matter source. The classic problem of Schiff is critically revisited.

scholarly journals A NEW LOOK AT THE PLEBAŃSKI–DEMIAŃSKI FAMILY OF SOLUTIONS

2006 ◽  
Vol 15 (03) ◽  
pp. 335-369 ◽  
Author(s):  
J. B. GRIFFITHS ◽  
J. PODOLSKÝ
Keyword(s):  
Electromagnetic Field ◽  
Angular Velocity ◽  
Physical Interpretation ◽  
Line Element ◽  
Coordinate Transformations ◽  
Entire Family ◽  
Type D ◽  
Special Cases ◽  
New Form ◽  
Two Parameters

The Plebański–Demiański metric, and those that can be obtained from it by taking coordinate transformations in certain limits, include the complete family of space–times of type D with an aligned electromagnetic field and a possibly non-zero cosmological constant. Starting with a new form of the line element which is better suited both for physical interpretation and for identifying different subfamilies, we review this entire family of solutions. Our metric for the expanding case explicitly includes two parameters which represent the acceleration of the sources and the twist of the repeated principal null congruences, the twist being directly related to both the angular velocity of the sources and their NUT-like properties. The non-expanding type D solutions are also identified. All special cases are derived in a simple and transparent way.

scholarly journals TWO LIMIT CASES OF BORN–INFELD EQUATIONS

2007 ◽  
Vol 04 (04) ◽  
pp. 565-586 ◽  
Author(s):  
YUE-JUN PENG ◽  
JÉRÉMY RUIZ
Keyword(s):  
Electric Field ◽  
Maxwell Equations ◽  
Space Dimension ◽  
Electromagnetic Theory ◽  
Lagrangian Systems ◽  
Compensated Compactness ◽  
Uniform Estimates ◽  
Low Field ◽  
Compactness Arguments ◽  
Magnetohydrodynamics System

We study two limit cases λ → ∞ and λ → 0 in Born–Infeld equations. Here the parameter λ > 0 is interpreted as the maximal electric field in the electromagnetic theory and the case λ = 0 corresponds to the string theory. Formal limits are governed by the classical Maxwell equations and pressureless magnetohydrodynamics system, respectively. For studying the limit λ → ∞, a new scaling is introduced. We give the relations between these limits and Brenier high and low field limits. Finally, using compensated compactness arguments, the limits are rigorously justified for global entropy solutions in L∞ in one space dimension, based on derived uniform estimates and techniques for linear Lagrangian systems.

scholarly journals The relation between Maxwell, Dirac, and the Seiberg-Witten equations

2003 ◽  
Vol 2003 (43) ◽  
pp. 2707-2734 ◽  
Author(s):  
Waldyr A. Rodrigues
Keyword(s):  
Spinor Field ◽  
Maxwell Equations ◽  
Degrees Of Freedom ◽  
Minkowski Spacetime ◽  
Magnetic Monopoles ◽  
The Other ◽  
Field Equations ◽  
Maxwell Theory ◽  
Hertz Potential ◽  
Form Field

We discuss unsuspected relations between Maxwell, Dirac, and the Seiberg-Witten equations. First, we present the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F=ψγ21ψ˜, where F is a given electromagnetic field. Such task is presented and it permits to clarify some objections to the MDE which claim that no MDE may exist because F has six (real) degrees of freedom and ψ has eight (real) degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth, even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form of the generalized Maxwell equations. One is the generalized Hertz potential field equation (which we discuss in detail) associated with Maxwell theory and the other is a (nonlinear) equation (of the generalized Maxwell type) satisfied by the 2-form field part of a Dirac-Hestenes spinor field that solves the Dirac-Hestenes equation for a free electron. This is a new result which can also be called MDE of the second kind. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime. A physical interpretation for those equations is proposed.

GEOMETRIZATION OF ELECTROMAGNETISM IN TETRAD-SPIN-CONNECTION GRAVITY

2009 ◽  
Vol 24 (06) ◽  
pp. 431-442 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Variational Principle ◽  
Electromagnetic Fields ◽  
Spinor Field ◽  
Maxwell Equations ◽  
Electromagnetic Coupling ◽  
Ricci Scalar ◽  
Spin Connection ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Generally Covariant

The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic fields is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational principle with the tetrad and spin connection as dynamical variables and show that, in this approach, the field equations are the Einstein–Maxwell equations if we relate the electromagnetic potential to the trace of the spin connection. We also show that, as in the Ponomarev–Obukhov formulation, the generally covariant Dirac Lagrangian gives rise to the standard spinor source for the Einstein–Maxwell equations, while the spinor field obeys the nonlinear Heisenberg–Ivanenko equation with the electromagnetic coupling. We generalize that formulation to spinors with arbitrary electric charges.

scholarly journals Emergence of maximal acceleration from non-commutativity of spacetime

2021 ◽  
pp. 2150069
Author(s):  
E. Harikumar ◽  
Leela Ganesh Chandra Lakkaraju ◽  
Vishnu Rajagopal
Keyword(s):  
Deformation Parameter ◽  
Line Element ◽  
Minkowski Spacetime ◽  
Geodesic Equation ◽  
Newtonian Limit ◽  
First Order ◽  
Maximal Acceleration

In this paper, we show that the causally connected four-dimensional line element of the [Formula: see text]-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Formula: see text]-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

scholarly journals Holomorphy in Pseudo-Euclidean Spaces and the Classic Electromagnetic Theory

2019 ◽  
Vol 7 (4) ◽  
pp. 27-36
Author(s):  
Vlad L. Negulescu
Keyword(s):  
Differential Equations ◽  
Maxwell Equations ◽  
Holomorphic Functions ◽  
Electromagnetic Theory ◽  
Space Time ◽  
Rotation Matrix ◽  
Euclidean Spaces ◽  
Charge Conservation

A new concept of holomorphy in pseudo-Euclidean spaces is briefly presented. The set of extended Cauchy-Riemannn differential equations, which are verified by the holomorphic functions, is obtained. A form of the general pseudo-rotation matrix was developed. The generalized d’Alembert- operator and extended Poisson’s equations are defined. Applying these results to the relativistic space-time, the charge conservation and general Maxwell equations are derived.

scholarly journals Maxwell Electrodynamics in Terms of Physical Potentials

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 915 ◽  
Author(s):  
Parthasarathi Majumdar ◽  
Anarya Ray
Keyword(s):  
Maxwell Equations ◽  
Minkowski Spacetime ◽  
Laplacian Operator ◽  
Charged Scalar ◽  
Gauge Invariant ◽  
Vector Potentials ◽  
Maxwell Electrodynamics ◽  
Gauge Fixing ◽  
Bohm Effect ◽  
Aharonov Bohm

A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov–Bohm effect, where dependence of the Aharonov–Bohm phase on the physical vector potential is highlighted.

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 CRITICISM OF "NECESSITY OF SIMULTANEOUS CO-EXISTENCE OF INSTANTANEOUS AND RETARDED INTERACTIONS IN CLASSICAL ELECTRODYNAMICS" BY CHUBYKALO AND VLAEV

2002 ◽  
Vol 17 (27) ◽  
pp. 3975-3979 ◽  
Author(s):  
J. D. JACKSON
Keyword(s):  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Electromagnetic Theory ◽  
Classical Electrodynamics ◽  
Lorentz Gauge ◽  
Vector Potentials ◽  
Electromagnetic Interactions ◽  
Derivatives Of ◽  
Made In

The demonstration that the electromagnetic fields derived from the Liénard–Wiechert potentials do not satisfy the Maxwell equations is proved to be false. Errors were made in the computation of the derivatives of retarded quantities. The subsequent inference of the necessity of both instantaneous and retarded electromagnetic interactions cannot be made. Different choices of gauge can lead to a variety of forms for the scalar and vector potentials, always with the same retarded fields. Classical electromagnetic theory is complete as usually expressed. One may choose to work in the Lorentz gauge in which all quantities are retarded.

CONFORMAL GRAVITY AND GRAVITATIONAL WAVES

2011 ◽  
Vol 20 (10) ◽  
pp. 1941-1943 ◽  
Author(s):  
LUCA FABBRI ◽  
M. B. PARANJAPE
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Invariant Theory ◽  
Minkowski Spacetime ◽  
Coordinate Transformations ◽  
Conformal Gravity ◽  
Conformally Invariant ◽  
Wave Solutions ◽  
Linearized Theory ◽  
Plane Gravitational Waves

We consider monochromatic, plane gravitational waves in a conformally invariant theory of general relativity. We show that the simple, standard ansatz for the metric, usually that which is taken for the linearized theory of these waves, is reducible to the metric of Minkowski spacetime via a sequence of conformal and coordinate transformations. This implies that we have in fact, exact plane wave solutions. However they are simply coordinate/conformal artifacts. As a consequence, they carry no energy.

Sign in / Sign up

Export Citation Format

Share Document