Singularity of electromagnetic field near the trajectory of point particles: the general case

1988 ◽  
Vol 66 (4) ◽  
pp. 289-291
Author(s):  
Bernard M. de Dormale
Keyword(s):  
Electromagnetic Field ◽  
Rest Frame ◽  
Inertial Frame ◽  
Radiation Reaction ◽  
Point Particle ◽  
Point Particles ◽  
Special Case

The singularity of the electromagnetic field created by a point particle has been investigated by Dirac in the special case where the trajectory is approached in the rest frame of the particle. His result, fundamental in the study of radiation reaction, is generalized here to the case of an arbitrary inertial frame.

scholarly journals An introduction to the Kaluza-Klein formulation

2020 ◽  
Vol 17 (1 Jan-Jun) ◽  
pp. 27
Author(s):  
G. F. Torres del Castillo
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Dimensional Space ◽  
Point Particle ◽  
Zero Field ◽  
Point Particles ◽  
Klein Gordon ◽  
Constants Of Motion ◽  
Common Misunderstanding ◽  
Kaluza Klein

We give an elementary introduction to the Kaluza-Klein formulation, in which the gravitational and the electromagnetic fields are represented in the geometry of a five-dimensional space. We show that, in the framework of general relativity, the interaction of a point particle, or of a charged spin-zero field, with a gravitational and an electromagnetic field can be obtained through the metric of a five-dimensional space. We also show that the symmetries of the metric of this five-dimensional space lead to constants of motion for the point particles, or to operators that commute with the Klein--Gordon operator. A common misunderstanding related to the unification of gravitation and electromagnetism given by the Kaluza--Klein formulation is discussed.

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

Field of a Uniformly Moving Charge in an Anisotropic Dispersive Medium

1973 ◽  
Vol 28 (6) ◽  
pp. 907-910
Author(s):  
S. Datta Majumdar ◽  
G. P. Sastry
Keyword(s):  
Electromagnetic Field ◽  
Fourier Transform ◽  
Point Charge ◽  
Rest Frame ◽  
Dispersive Medium ◽  
Scalar Potential ◽  
Fourier Integral ◽  
The Third ◽  
Dispersion Formula ◽  
The Fourier Transform

The electromagnetic field of a point charge moving uniformly in a uniaxial dispersive medium is studied in the rest frame of the charge. It is shown that the Fourier integral for the scalar potential breaks up into three integrals, two of which are formally identical to the isotropic integral and yield the ordinary and extraordinary cones. Using the convolution theorem of the Fourier transform, the third integral is reduced to an integral over the isotropic field. Dispersion is explicitly introduced into the problem and the isotropic field is evaluated on the basis of a simplified dispersion formula. The effect of dispersion on the field cone is studied as a function of the cut-off frequency.

scholarly journals Geodesies of an affine connection and electromagnetism with radiation reaction

1971 ◽  
Vol 4 (2) ◽  
pp. 225-240 ◽  
Author(s):  
R.R. Burman
Keyword(s):  
Electromagnetic Field ◽  
Affine Connection ◽  
Radiation Reaction ◽  
External Electromagnetic Field ◽  
Geodesic Equation ◽  
Conformally Flat ◽  
Metric Tensor ◽  
Special Cases ◽  
Test Charge ◽  
Point Test

This paper deals with the motion of a point test charge in an external electromagnetic field with the effect of electromagnetic radiation reaction included. The equation of motion applicable in a general Riemannian space-time is written as the geodesic equation of an affine connection. The connection is the sum of the Christoffel connection and a tensor which depends on, among other things, the external electromagnetic field, the charge and mass of the particle and the Ricci tensor. The affinity is not unique; a choice is made so that the covariant derivative of the metric tensor with respect to the connection vanishes. The special cases of conformally flat spaces and the space of general relativity are discussed.

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

scholarly journals THE LIENARD–WIECHERT POTENTIAL OF CHARGED SCALAR PARTICLES AND THEIR RELATION TO SCALAR ELECTRODYNAMICS IN THE REST-FRAME INSTANT FORM

1998 ◽  
Vol 13 (16) ◽  
pp. 2791-2831 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Rest Frame ◽  
Coulomb Gauge ◽  
Charged Scalar ◽  
Scalar Particles ◽  
Field System ◽  
Instant Form ◽  
Hamilton Equations ◽  
New Type

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard–Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham–Lorentz–Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach–Villars formalism, the connection with the particle plus electromagnetic field system is found.

scholarly journals Comparison of Different Forms for the “Spin” and “Orbital” Components of the Angular Momentum of Light

2011 ◽  
Vol 2011 ◽  
pp. 1-4 ◽  
Author(s):  
A. M. Stewart
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Inertial Frame ◽  
Classical Electrodynamics

We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an “orbital” and “spin” nature. All three expressions are different, and there seems to be no reason to prefer one to another. It appears, on the basis of classical electrodynamics, that there is no unique way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in a fixed inertial frame.

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