scholarly journals Extended Lorentz-force-like equation and electromagnetic field tensor as consequence of a spinorial structure of space-time

2007 ◽  
Vol 66 ◽  
pp. 012017
Author(s):  
Hajjawi S ◽  
Buitrago J
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Force ◽  
Space Time ◽  
Field Tensor ◽  
Electromagnetic Field Tensor

scholarly journals Lorentz force and ponderomotive force in the presence of a minimal length

2016 ◽  
Vol 14 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Behrooz Khosropour
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Force ◽  
Uncertainty Principle ◽  
Upper Bound ◽  
Ponderomotive Force ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Field Tensor ◽  
Faraday’S Law ◽  
Electromagnetic Field Tensor

In this work, according to the electromagnetic field tensor in the framework of generalized uncertainty principle (GUP), we obtain the Lorentz force and Faraday’s law of induction in the presence of a minimal length. Also, the ponderomotive force and ponderomotive pressure in the presence of a measurable minimal length are found. It is shown that in the limit [Formula: see text], the generalized Lorentz force and ponderomotive force become the usual forms. The upper bound on the isotropic minimal length is estimated.

Electromagnetism and special relativity

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Point Charge ◽  
Reference Frames ◽  
Classical Electrodynamics ◽  
Covariant Form ◽  
Field Tensor ◽  
Electromagnetic Field Tensor ◽  
Preferred Reference Frame ◽  
Physical Quantities

In 1905, when Einstein published his theory of special relativity, Maxwell’s work was already about forty years old. It is therefore both remarkable and ironic (recalling the old arguments about the aether being the ‘preferred’ reference frame for describing wave propagation) that classical electrodynamics turned out to be a relativistically correct theory. In this chapter, a range of questions in electromagnetism are considered as they relate to special relativity. In Questions 12.1–12.4 the behaviour of various physical quantities under Lorentz transformation is considered. This leads to the important concept of an invariant. Several of these are encountered, and used frequently throughout this chapter. Other topics considered include the transformationof E- and B-fields between inertial reference frames, the validity of Gauss’s law for an arbitrarily moving point charge (demonstrated numerically), the electromagnetic field tensor, Maxwell’s equations in covariant form and Larmor’s formula for a relativistic charge.

scholarly journals Toward Nonlocal Electrodynamics of Accelerated Systems

Universe ◽  
2020 ◽  
Vol 6 (12) ◽  
pp. 229
Author(s):  
Bahram Mashhoon
Keyword(s):  
Electromagnetic Field ◽  
Parity Violation ◽  
Spin Rotation ◽  
Field Tensor ◽  
Parity Conservation ◽  
Electromagnetic Field Tensor ◽  
Nonlocal Electrodynamics

We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the field kernel in the acceleration tensor. However, we show that parity conservation can be maintained by extending the field kernel to include quadratic terms in the acceleration tensor. The field kernel must vanish in the absence of acceleration; otherwise, a general dependence of the kernel on the acceleration tensor cannot be theoretically excluded. The physical implications of the quadratic kernel are briefly discussed.

scholarly journals THE MAXWELL LAGRANGIAN IN PURELY AFFINE GRAVITY

2008 ◽  
Vol 23 (03n04) ◽  
pp. 567-579 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Electromagnetic Field ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Legendre Transformation ◽  
Conformal Transformations ◽  
Field Tensor ◽  
Metric Tensor ◽  
Hamiltonian Density ◽  
Electromagnetic Field Tensor ◽  
Affine Gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic curvature, is dynamically equivalent to the Einstein–Maxwell equations in the metric–affine and metric formulation. We show that this equivalence is related to the invariance of the Maxwell Lagrangian under conformal transformations of the metric tensor. We also apply to a purely affine Lagrangian the Legendre transformation with respect to the tensor of homothetic curvature to show that the corresponding Legendre term and the new Hamiltonian density are related to the Maxwell–Palatini Lagrangian for the electromagnetic field. Therefore the purely affine picture, in addition to generating the gravitational Lagrangian that is linear in the curvature, justifies why the electromagnetic Lagrangian is quadratic in the electromagnetic field.

On a duality invariant action principle in vacuum electrodynamics

1970 ◽  
Vol 48 (20) ◽  
pp. 2423-2426 ◽  
Author(s):  
G. M. Levman
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Lagrangian Density ◽  
Vacuum Field ◽  
Field Tensor ◽  
Field Equations ◽  
Invariant Action ◽  
Electromagnetic Field Tensor ◽  
Derivatives Of

Although Maxwell's vacuum field equations are invariant under the so-called duality rotation, the usual Lagrangian density for the electromagnetic field, which is bilinear in the first derivatives of the electromagnetic potentials, does not exhibit that invariance. It is shown that if one takes the components of the electromagnetic field tensor as field variables then the most general Lorentz invariant Lagrangian density bilinear in the electromagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations.

scholarly journals EFFECTIVE DYNAMICS FOR SOLITONS IN THE NONLINEAR KLEIN–GORDON–MAXWELL SYSTEM AND THE LORENTZ FORCE LAW

2009 ◽  
Vol 21 (04) ◽  
pp. 459-510 ◽  
Author(s):  
EAMONN LONG ◽  
DAVID STUART
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Force ◽  
Scalar Fields ◽  
Space Time ◽  
Maxwell System ◽  
Complex Scalar ◽  
Effective Dynamics ◽  
Dimensional Minkowski Space ◽  
Klein Gordon ◽  
Lorentz Force Law

We consider the nonlinear Klein–Gordon–Maxwell system derived from the Lagrangian [Formula: see text] on four-dimensional Minkowski space-time, where ϕ is a complex scalar field and Fμν = ∂μ𝔸ν - ∂ν𝔸μ is the electromagnetic field. For appropriate nonlinear potentials [Formula: see text], the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current 𝕁B, and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external electromagnetic fields are O(1), but vary slowly over space-time scales of [Formula: see text], and δ = e1 - k for [Formula: see text] as e → 0. We work entirely in the energy norm, and the approximation is controlled in this norm for times of [Formula: see text].

THE DYNAMICAL THEORY OF MAGNETIC MONOPOLES

1952 ◽  
Vol 30 (3) ◽  
pp. 218-225 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Electromagnetic Field ◽  
Equations Of Motion ◽  
Natural Generalization ◽  
Magnetic Monopoles ◽  
Dynamical Theory ◽  
The Other ◽  
Field Tensor ◽  
Physical Content ◽  
Electromagnetic Field Tensor ◽  
Set Up

The theory of electric charges and magnetic monopoles has been set up by Dirac by expressing the electromagnetic field tensor in terms of one four-potential and of the variables describing the strings attached to each magnetic mono-pole. In this reformulation of Dirac's theory the field tensor is expressed in terms of two four-potentials, one corresponding to charges and the other to monopoles, and the action principle for the equations of motion is set up in terms of the two four-potentials and of the tensors dual to them. Thus there is formal symmetry as far as is possible in the treatment of the charges and the monopoles. Also the mathematics is direct and neat. Though the physical content is the same as that of Dirac, a natural generalization of the Fermi form of electrodynamics subject to the restriction that the same particle cannot have both charge and monopole is obtained here.

THE RESOLUTION OF FOUR-DIMENSIONAL VECTOR FIELD AND TENSOR FIELDS, AND ITS APPLICATION TO ELECTRODYNAMICS

1955 ◽  
Vol 33 (5) ◽  
pp. 235-240
Author(s):  
N. L. Balazs
Keyword(s):  
Electromagnetic Field ◽  
Potential Field ◽  
Vector Fields ◽  
Dimensional Vector ◽  
Field Tensor ◽  
Algebraic Condition ◽  
Tensor Fields ◽  
Lorentz Condition ◽  
Electromagnetic Field Tensor ◽  
Magnetic Poles

We generalize Helmholtz's theorem and apply it to four-dimensional vector fields and tensor fields. For vector fields the generalization is straightforward. Antisymmetric tensor fields of rank two exhibit a beautiful symmetry between the irrotational part of the tensor and the dual of the solenoidal component. The physical applications show that in Maxwell's theory the irrotational part of the four-potential field has no physical meaning and the Lorentz condition makes it identically zero. In Dirac's new electrodynamics an algebraic condition is imposed on the four-potential. Hence in this theory the irrotational part is not zero, and the algebraic condition establishes a relation between the sources and vortices of the four-potential field. If we apply the resolution to the electromagnetic field tensor we can see that the free charges are responsible for the sources, and the magnetic poles, if they exist, for the vortices, provided we use the customary association between the components of the electromagnetic field tensor and the components of the electric and magnetic fields.

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