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 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.

scholarly journals VARIATIONAL FORMULATION OF EISENHART'S UNIFIED THEORY

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3975-3984
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
Variational Formulation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Affine Connection ◽  
Unified Theory ◽  
Field Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field ◽  
Electromagnetic Field Tensor

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.

On Killing vectors and invariance transformations of the Einstein–Maxwell equations

1976 ◽  
Vol 80 (2) ◽  
pp. 357-364 ◽  
Author(s):  
M. L. Woolley
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Invariance Group ◽  
Field Tensor ◽  
Metric Tensor ◽  
Divergence Free Vector ◽  
Point Transformations ◽  
Maxwell Space ◽  
Electromagnetic Field Tensor ◽  
Simply Connected

AbstractIt is shown that, in a simply connected four dimensional Riemannian space, an arbitrary divergence-free vector generates a one-parameter group of point transformations which leaves Maxwell's equations unchanged. This result is used to show that, if the metric tensor of a simply connected vacuum Einstein–Maxwell space-time admits a group of motions which is also an invariance group of the electromagnetic field tensor, then there exists a one-parameter family of metric tensors all of which satisfy the Einstein–Maxwell equations with the invariant electromagnetic field as source.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

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.

Analysis on Lightning Electromagnetic Fields

2013 ◽  
Vol 401-403 ◽  
pp. 350-353 ◽  
Author(s):  
Pi Cui Zhang ◽  
Wei He ◽  
Liu Ling Wang ◽  
Li Feng Ma
Keyword(s):  
Electromagnetic Field ◽  
Spatial Distribution ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Practical Significance ◽  
Lightning Protection ◽  
Perfect Conductor ◽  
Fundamental Theory ◽  
Lightning Current ◽  
The Earth

t is generally needed to know precisely spatial distribution of lightning electromagnetic fields in the lightning protection measurements. Therefore, the research on the lightning electromagnetic field is of practical significance. In this paper, the Maxwell equations were used to calculate and analyze the spatial distribution of lightning electromagnetic fields surrounding lightning current. And the expressions of lightning current electromagnetic fields were deduced under the assumption that the earth was under the condition of perfect conductor. The spatial distributions of the components of lightning electromagnetic fields have been plotted by Matlab. The results would provide fundamental theory for the research of lightning electromagnetic field and lightning protection measurements.

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 Solitary Waves in Abelian Gauge Theories

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Vieri Benci ◽  
Donato Fortunato
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Solitary Waves ◽  
Lower Order ◽  
Gauge Theories ◽  
Order Term ◽  
Lower Order Term ◽  
Field Equations ◽  
Abelian Gauge ◽  
Physical Phenomena

AbstractAbelian gauge theories consist of a class of field equations which provide a model for the interaction between matter and electromagnetic fields. In this paper we analyze the existence of solitary waves for these theories. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and electromagnetic field is small. We point out that the positiveness assumption on W implies that the energy is positive: this fact makes these theories more suitable to model physical phenomena.

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