An attempt to geometrize electromagnetism

AbstractThis study investigates the curved worldline of a charged particle accelerated by an electromagnetic field in flat spacetime. A new metric, which dependes on the charge-to-mass ratio and electromagnetic potential, is proposed to describe the curve characteristic of the world-line. The main result of this paper is that an equivalent equation of the Lorentz equation of motion is put forward based on a 4-dimensional Riemannian manifold defined by the metric. Using the Ricci rotation coefficients, the equivalent equation is self-consistently constructed. Additionally, the Lorentz equation of motion in the non-inertial reference frames is studied with the local Lorentz covariance of the equivalent equation. The model attempts to geometrize classical electromagnetism in the absence of the other interactions, and it is conducive to the establishment of the unified theory between electromagnetism and gravitation.

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Classical electrodynamics: the equation of motion

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100048994 ◽

1974 ◽

Vol 76 (1) ◽

pp. 359-367 ◽

Cited By ~ 4

Author(s):

P. A. Hogan

Keyword(s):

Electromagnetic Field ◽

Charged Particle ◽

Scalar Field ◽

World Line ◽

External Electromagnetic Field ◽

Equation Of Motion ◽

The Self ◽

Classical Electrodynamics ◽

Field Equations ◽

The World

In this paper we derive the Lorentz-Dirac equation of motion for a charged particle moving in an external electromagnetic field. We use Maxwell's electromagnetic field equations together with the assumptions (1) that all fields are retarded and (2) that the 4-force acting on the charged particle is a Lorentz 4-force. To define the self-field on the world-line of the charge we utilize a contour integral representation for the field due to A. W. Conway. This by-passes the need to define an ‘average field’. In an appendix the case of a scalar field is briefly discussed.

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Ein klassisches Teilchenmodell mit variablem Gravitationskoeffizienter

Zeitschrift für Naturforschung A ◽

10.1515/zna-1962-0704 ◽

1962 ◽

Vol 17 (7) ◽

pp. 554-558

Author(s):

Jochen Lindner

Keyword(s):

Coulomb Field ◽

Coulomb Force ◽

Equation Of Motion ◽

Great Distance ◽

Classical Particle ◽

Unified Theory ◽

Specific Charge ◽

Field Function ◽

Typical Function ◽

Theory Of Gravitation

The unified theory of gravitation and the electromagnetic field in the form suggested by BECHERT 1 has solutions which correspond to the model of a classical particle of mass Moo and charge Q. We shall assume that the coefficient of gravitation χ is not a constant but a field function. The equation of motion is derived for this case. It shows that a suitable choice of the field function χ leads to a correct COULOMB field as well as to a correct gravitational field (corresponding to Q and Mo) in great distance from the particle. The extension of the particle is characterized by the classical radius L=Q2/Moc2 of the particle, it holds together by the balance between COULOMB force and gravitation. The specific charge turns out to be a typical function of the distance from the center of the particle.

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Lorentz Atom Revisited by Solving the Abraham–Lorentz Equation of Motion

Zeitschrift für Naturforschung A ◽

10.1515/zna-2017-0182 ◽

2017 ◽

Vol 72 (8) ◽

pp. 717-731 ◽

Cited By ~ 1

Author(s):

Jürgen Bosse

Keyword(s):

Steady State Solution ◽

Equation Of Motion ◽

Photon Absorption ◽

Forced Oscillations ◽

Quantum Mechanical ◽

Quantum Oscillator ◽

Great Success ◽

Deep Insight ◽

Lorentz Equation ◽

Insight Into

AbstractBy solving the non-relativistic Abraham–Lorentz (AL) equation, I demonstrate that the AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however, for deducing the appropriate parameters Ω and Γ to be used with the equation of forced oscillations in modelling the Lorentz atom. The electric polarisability, which many authors “derived” from the AL equation in recent years, is shown to violate Kramers–Kronig relations rendering obsolete the extracted photon-absorption rate, for example. Fortunately, errors turn out to be small quantitatively, as long as the light frequency ω is neither too close to nor too far from the resonance frequency Ω. The polarisability and absorption cross section are derived for the Lorentz atom by purely classical reasoning and are shown to agree with the quantum mechanical calculations of the same quantities. In particular, oscillator parameters Ω and Γ deduced by treating the atom as a quantum oscillator are found to be equivalent to those derived from the classical AL equation. The instructive comparison provides a deep insight into understanding the great success of Lorentz’s model that was suggested long before the advent of quantum theory.

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Generalized abelian gauge field theory under rotor model

Modern Physics Letters A ◽

10.1142/s0217732321501947 ◽

2021 ◽

Vol 36 (27) ◽

pp. 2150194

Author(s):

B. T. T. Wong

Keyword(s):

Field Theory ◽

Gauge Field ◽

Equation Of Motion ◽

Gauge Field Theory ◽

Quantum Field ◽

Abelian Gauge ◽

Flat Spacetime ◽

Rank One ◽

Strength Formula ◽

Rotor Model

Gauge field theory with rank-one field [Formula: see text] is a quantum field theory that describes the interaction of elementary spin-1 particles, of which being massless to preserve gauge symmetry. In this paper, we give a generalized, extended study of abelian gauge field theory under successive rotor model in general [Formula: see text]-dimensional flat spacetime for spin-1 particles in the context of higher-order derivatives. We establish a theorem that [Formula: see text] rotor contributes to the [Formula: see text] fields in the integration-by-parts formalism of the action. This corresponds to the transformation of gauge field [Formula: see text] and gauge field strength [Formula: see text] in the action. The [Formula: see text] case restores back to the standard abelian gauge field theory. The equation of motion and Noether’s conserved current of the theory are also studied.

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Electromagnetic energy tensors and the Lorentz equation of motion for fields with electric and magnetic charge distributions

Journal of Mathematical Physics ◽

10.1063/1.525351 ◽

1982 ◽

Vol 23 (2) ◽

pp. 293-295

Author(s):

J. M. Nevin

Keyword(s):

Magnetic Charge ◽

Equation Of Motion ◽

Electromagnetic Energy ◽

Charge Distributions ◽

Lorentz Equation

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Dynamics of a point particle

10.1093/oso/9780198786399.003.0024 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

External Field ◽

Conservation Law ◽

Short Range ◽

Reference Frames ◽

World Line ◽

Inertial Mass ◽

Momentum Conservation ◽

Point Particle ◽

Mass Energy ◽

Internal Forces

This chapter attributes an inertial ‘mass–energy’ to particles. It also distinguishes between the action of an external field and of long-range and short-range internal forces, which is useful for establishing the laws of dynamics of an interacting body—that is, the equations determining its world line. The chapter also presents the 4-momentum conservation law for massive particles and light particles in inertial reference frames. It then gives some examples which illustrate the role played by this law in collisions. Finally, the chapter illustrates the conservation law by the Compton experiment, that is, the collision of a light corpuscle with a particle, and the concept of the quantum of action that can be derived from it.

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