The classical equations of motion of an electron

1946 ◽  
Vol 42 (3) ◽  
pp. 278-286 ◽  
Author(s):  
C. Jayaratnam Eliezer
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Cross Section ◽  
Equations Of Motion ◽  
Conservation Of Energy ◽  
Scattering Of Light ◽  
Dirac Equations ◽  
Symmetrical Form ◽  
Usual Scheme

A set of relativistic classical motions of a radiating electron in an electromagnetic field are derived from the principle of conservation of energy, momentum and angular momentum. It is shown that these equations lead to results more in harmony with the usual scheme of mechanics than do the Lorentz-Dirac equations. When applied to discuss the motion of the electron of the hydrogen atom, these equations permit the electron falling into the nucleus, whereas the Lorentz-Dirac equations do not allow this. When applied to consider the motion of an electron which is disturbed by a pulse of radiation, the solution is in a more symmetrical form. For scattering of light of frequency ν the expression for the scattering cross-section is found to be the same as the classical Thomson formula for small ν, and to vary as ν−4 for large ν.

scholarly journals On the classical theory of particles

1948 ◽  
Vol 194 (1039) ◽  
pp. 543-555 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Cross Section ◽  
Classical Theory ◽  
Incident Light ◽  
Equations Of Motion ◽  
Universal Constant ◽  
External Electromagnetic Field ◽  
Dirac Equations ◽  
Lorentz Theory ◽  
Relativistic Equations

A set of classical relativistic equations of motion of an electron in an electromagnetic field is postulated. These equations are free from ‘run-away’ solutions, and give the same results as the Maxwell-Lorentz theory for non-relativistic motions when the external electromagnetic field does not vary too rapidly. For the scattering of light by an electron, the scattering crosssection is independent of the frequency and is a universal constant. This brings out a point of difference from the Lorentz-Dirac equations according to which the scattering cross-section varies inversely as the square of the frequency of the incident light, for large frequencies. For the motion of an electron towards a fixed proton, the equations allow a collision, unlike the Lorentz-Dirac equations according to which the electron is brought to rest before it reaches the proton.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

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.

Electron – hydrogen atom collision in the presence of a circularly polarized laser field

1979 ◽  
Vol 57 (11) ◽  
pp. 1886-1889 ◽  
Author(s):  
H. G. P. Lins de Barros ◽  
H. S. Brandi
Keyword(s):  
Electromagnetic Field ◽  
Hydrogen Atom ◽  
Cross Section ◽  
Laser Field ◽  
Excitation Cross Section ◽  
Scattering Amplitude ◽  
Circularly Polarized ◽  
Field Polarization ◽  
Oppenheimer Approximation ◽  
Atom Collision

Electron–hydrogen collision in the presence of a circularly polarized laser field is studied within a formalism based in an appropriate space-translations transformation and the Green's function formalism. The Born–Oppenheimer approximation for the scattering amplitude is obtained and the dependence of the differential and total excitation cross section on the electromagnetic field polarization is studied.

The influence of radiation damping on the scattering of light and mesons by free particles. I

1941 ◽  
Vol 37 (3) ◽  
pp. 291-300 ◽  
Author(s):  
W. Heitler
Keyword(s):  
Cross Section ◽  
Free Electron ◽  
Light Wave ◽  
Equation Of Motion ◽  
Radiation Damping ◽  
Conservation Of Energy ◽  
Scattering Of Light ◽  
Relativistic Approximation ◽  
Free Particles ◽  
Image Position

1. In the classical theory there is no difficulty in treating the effect of radiation damping on the scattering of light by a free electron in so far as it is a result of the conservation of energy. In the non-relativistic approximation the equation of motion of a free electron under the influence of a light wave iswith the periodic solution The total energy radiated per second is thenand the total cross-section(1) isFormula (1) differs from the Thomson formula by the factor 1/(1 +κ2). This factor becomes appreciable for energies ħν ≥ 137mc2.

A Method for Testing Numerical Integrations of Equations of Motion of Mechanical Systems

1988 ◽  
Vol 55 (3) ◽  
pp. 711-715 ◽  
Author(s):  
T. R. Kane ◽  
D. A. Levinson
Keyword(s):  
Angular Momentum ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Test Results ◽  
Conservation Of Energy ◽  
Testing Method ◽  
Conservation Principle ◽  
Numerical Integrations ◽  
Conservation Principles

It is common practice to use conservation principles, such as the principles of conservation of energy or angular momentum, to test results of numerical integrations of differential equations of motion of mechanical systems. This paper deals with a testing method that can be used even when no conservation principle is applicable.

On the classical theory of radiating electrons

1945 ◽  
Vol 41 (2) ◽  
pp. 184-186 ◽  
Author(s):  
C. Jayaratnam Eliezer ◽  
A. W. Mailvaganam
Keyword(s):  
Electromagnetic Field ◽  
Classical Theory ◽  
Proper Time ◽  
Equations Of Motion ◽  
Spherical Model ◽  
Flat Space ◽  
External Electromagnetic Field ◽  
Radiation Damping ◽  
Conservation Of Energy ◽  
Image Position

1. In Dirac's classical theory of radiating electrons, the relativistic equations of motion of a point-electron in an electromagnetic field arewhere (x0, x1, x2, x3) denote the electron's coordinates in flat space-time, dots denote differentiation with respect to the proper time , and the external electromagnetic field is described by the usual field quantities Fμν. The units are chosen so that the velocity of light is unity. These equations, which are derived from the principles of conservation of energy and of momentum, are the same as those obtained by Lorentz, when he used the spherical model of the electron and included radiation damping in an approximate way. But Dirac's method of derivation suggests that this treatment of radiation damping, and therefore the resulting scheme of equations, is exact within the limits of the classical theory.

On the theory of spinning particles

1947 ◽  
Vol 43 (1) ◽  
pp. 106-117 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Quantum Theory ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Hamiltonian Equation ◽  
Hamiltonian Form ◽  
Spin Angular Momentum ◽  
Spinning Particle

A classical theory of a spinning particle with charge and dipole moment in an electromagnetic field is obtained by working symmetrically with respect to retarded and advanced fields, and with respect to the ingoing and outgoing fields. The equations are in a simpler form than those of Bhabha and Corben or those of Bhabha, and involve fewer constants. On the assumption that the spin angular momentum tensor θμν satisfies the equation θ2 ≡ θμν θμν = constant, the value of the dipole moment Zμν is chosen to be Cθμν, where C is a constant. The theory is generalized to the case of several particles with charge and dipole moment. By using a suitable Hamiltonian equation, the classical equations of motion, obtained on the assumption that θ is a constant, are put into Hamiltonian form by means of the ‘Wentzel field’ and the λ-limiting process. The passage to the quantum theory is effected by the usual rules of quantization. The theory is extended to the case of particles with charge and dipole moment in the generalized wave field by defining the Wentzel potential in terms of the generalized relativistic δ-function.

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

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