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.

The eigenvalues of electromagnetic angular momentum

1936 ◽  
Vol 32 (4) ◽  
pp. 614-621 ◽  
Author(s):  
M. H. L. Pryce
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Vector Potential ◽  
Charged Particles ◽  
Radial Component ◽  
Spin Angular Momentum ◽  
The Magnetic Field ◽  
Field Strengths

It is shown that the eigenvalues of the angular momentum of the electromagnetic field containing a number of charged particles, apart from spin angular momentum, are only the integral multiples of ħ. This is shown by using cylindrical polar variables, and taking a particular choice of the vector potential in which the radial component is zero, defined explicitly in terms of the magnetic field strengths. By expanding in terms of the Fourier functions einθ, the angular momentum is separated out into terms independent of one another, each taking on only integral values in units of ħ.The arguments all apply equally well to a modified field theory such as that of Born and Infeld.

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.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Equations Of Motion ◽  
Geodesic Equation ◽  
First Integrals ◽  
Spacetime Symmetries ◽  
Conserved Quantities ◽  
Killing Vectors ◽  
Invariance Properties ◽  
Matter Energy

This chapter studies how the ‘spacetime symmetries’ can generate first integrals of the equations of motion which simplify their solution and also make it possible to define conserved quantities, or ‘charges’, characterizing the system. As already mentioned in the introduction to matter energy–momentum tensors in Chapter 3, the concepts of energy, momentum, and angular momentum are related to the invariance properties of the solutions of the equations of motion under spacetime translations or rotations. The chapter explores these in greater detail. It first turns to isometries and Killing vectors. The chapter then examines the first integrals of the geodesic equation, and Noether charges.

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.

scholarly journals On the conservation of momentum

1946 ◽  
Vol 186 (1007) ◽  
pp. 432-442
Keyword(s):  
Angular Momentum ◽  
Potential Energy ◽  
Body Problem ◽  
Equations Of Motion ◽  
Gravitational Theory ◽  
Gravitational Potential Energy ◽  
Many Body ◽  
Conservation Of Momentum ◽  
The Many ◽  
The Universe

1. Scope of the paper . The present paper is a continuation of an earlier sequence in these Proceedings , entitled ‘ The inverse square law of gravitation, I, II and III’ (Milne 1936, 1937c), which itself was connected with another sequence entitled ‘Kinematics, dynamics and the scale of time, I, II and III ’(Milne 1937 a,b ). In the latter sequence the relations between t -dynamics and r -dynamics were obtained. In the former sequence a formula for the gravitational potential energy of two particles was isolated which was Lorentz-invariant for transformations from any one fundamental observer in the expanding substratum to any other fundamental observer; and the corresponding equations of motion in t -measure were obtained. In the present paper I obtain relations which correspond to the integrals of linear and angular momentum in the many-body problem of classical gravitational theory. I conclude that Einstein’s form of the conservation of linear momentum in special relativity holds good in the universe at large only in the case of a collinear set of particles moving along their line of collinearity, and I give the modification of the law of conservation which should hold good in other cases.

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

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