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.

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.

scholarly journals A connection between linearized Gauss–Bonnet gravity and classical electrodynamics II: Complete dual formulation

2021 ◽  
pp. 2150030
Author(s):  
Mark Robert Baker
Keyword(s):  
Field Strength ◽  
Gauge Theories ◽  
Equations Of Motion ◽  
Classical Electrodynamics ◽  
Necessary Condition ◽  
Property A ◽  
Gauge Invariant ◽  
Bonnet Gravity ◽  
Dual Formulation ◽  
Higher Spin

In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for [Formula: see text] and linearized Gauss–Bonnet gravity for [Formula: see text]. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in [Formula: see text] can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-[Formula: see text] curvature tensors for all [Formula: see text] are the field strength tensors for each [Formula: see text]. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

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.

Geometric phases modified by a Lorentz-symmetry violation background

2015 ◽  
Vol 30 (14) ◽  
pp. 1550072 ◽  
Author(s):  
L. R. Ribeiro ◽  
E. Passos ◽  
C. Furtado ◽  
J. R. Nascimento
Keyword(s):  
Electromagnetic Field ◽  
Geometric Phase ◽  
Quantum Dynamics ◽  
Dipole Moments ◽  
External Electromagnetic Field ◽  
Lorentz Symmetry ◽  
Nonrelativistic Quantum ◽  
Symmetry Violation ◽  
Electric Dipole Moments ◽  
Geometric Phases

We analyze the nonrelativistic quantum dynamics of a single neutral spin-half particle, with nonzero magnetic and electric dipole moments, moving in an external electromagnetic field in the presence of a Lorentz-symmetry violating background. We also study the geometric phase for this model taking in account the influence of the parameter that breaks the Lorentz-symmetry. These geometric phases are used to impose an upper bound on the background magnitude.

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 Helicity and Spin of Linearly Polarized Hermite-Gaussian Modes

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
M. Fernandez-Guasti ◽  
J. Hernández
Keyword(s):  
Angular Momentum ◽  
Continuity Equation ◽  
Orbital Momentum ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum ◽  
Linearly Polarized

The angular momentum content and propagation of linearly polarized Hermite-Gaussian modes are analyzed. The helicity gauge invariant continuity equation reveals that the helicity and flow in the direction of propagation are zero. However, the helicity flow exhibits nonvanishing transverse components. These components have been recently described as photonic wheels. These intrinsic angular momentum terms, depending on the criterion, can be associated with spin or orbital momentum. The electric and magnetic contributions to the optical helicity will be shown to cancel out for Hermite-Gaussian modes. The helicity ϱAC here derived is consistent with the interpretation that it represents the projection of the angular momentum onto the direction of motion.

scholarly journals Intrinsic angular momentum of the electromagnetic field

1992 ◽  
Vol 10 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Deng Ximing
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Hydrodynamic Model ◽  
Orbital Motion ◽  
Spin Angular Momentum ◽  
Number Operator ◽  
Conservation Property ◽  
Intrinsic Angular Momentum ◽  
Intrinsic Motion ◽  
Imaginary Number

The main point of the hydrodynamic model of the electromagnetic field (Deng Ximing & Fang Honglie 1979, 1980) is that the motion of the electromagnetic field can be divided into two parts: orbital motion and intrinsic motion. This paper defines an intrinsic angular momentum deduced from the intrinsic motion and a related Î (imaginary number) operator, whose basic properties are discussed. In addition, the conservation property of the intrinsic angular momentum and the relation between it and the spin angular momentum of the electromagnetic field are described.

THE ANGULAR MOMENTUM OF THE ELECTRON IN CLASSICAL ELECTRODYNAMICS

1950 ◽  
Vol 28a (3) ◽  
pp. 336-338
Author(s):  
F. A. Kaempffer
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Moment ◽  
Rest Mass ◽  
Classical Electrodynamics ◽  
G Factor ◽  
The Law

It is shown that not only the rest-mass of the electron but its spin as well is carried by the surrounding electromagnetic field. The ratio of magnetic moment and angular momentum (g-factor) of the electron is determined. The law of conservation of angular momentum is checked.

CENTER OF MASS AND SPIN FOR AXIALLY SYMMETRIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 717-728 ◽  
Author(s):  
CARLOS KOZAMEH ◽  
RAUL ORTEGA ◽  
TERESITA ROJAS
Keyword(s):  
Angular Momentum ◽  
Gravitational Radiation ◽  
Total Angular Momentum ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Intrinsic Angular Momentum

We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

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.

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