Electrodynamics, charged particles

The concept of A 3 can also be used to suggest a way out of the Dirac paradox [41] of U(l) electrodynamics, in which Dirac maintains that so long as we are dealing with transverse waves, we cannot bring in the Coulomb interaction between charged particles. In 0(3) electrodynamics, there is a force given by... 

In formulating quantum electrodynamics (QED), it has been found convenient to introduce the electromagnetic interaction with charged particles via the potentials instead of the fields. Consider a particle of charge q traveling on some path P from i to 2. Then the magnetic change in phase of the wavefunction is just... 

There are therefore obvious points of similarity between the 0(3) theory of electrodynamics and the Yang-Mills theory [44], Both are based, as we have argued, on an 0(3) or SU(2) invariant Lagrangian. However, in 0(3) electrodynamics, the particle concomitant with the field has the topological charge k/A(0>. In 0(3) electrodynamics, the internal space and spacetime are not independent spaces but form an extended Lie algebra [42], In elementary particle... 

This is the Abelian theory of quantum electrodynamics as a free field uncoupled to charged particles and fermions. 

This is an introduction to the sort of process that may occur in 0(3>)b electrodynamics. In effect, the B 3 field produces quantum vortices that interact with electrons, as well as other charged particles, where these vortices are quantized states and exist as fluctuations in the QED vacuum. As mentioned earlier the dual of the B 3 field does not exist as an electric field. These quantum fluctuations are easily seen to be associated with the and E fields ... 

Quantum electrodynamics involves the interaction of electrons, or other charged particles, and photons, where the interaction between two electrons involves the... 

Woolley, R. G. Charged particles, gauge invariance and molecular electrodynamics, IntJ. Quant. Chem., 74 (1999) 531-545. 

The electrodynamic balance (EDB) is a modern version of the Millikan oil drop apparatus in which a charged particle is levitated in an electric field [20]. By using quadrupole focusing, it is possible to suspend a single particle in a controlled environment virtually indefinitely. The size of a levitated particle can be measured by a variety of methods, the most precise of which uses the information contained in the resonant structure of light... 

The early practitioners and developers of density functional theory encountered yet another problem related to the extended nature of the number density primitive— self-interaction (Dreizler and Gross 1990, op. cit ). Specialized correction procedures were developed quite successfully and are in use in all modern calculations. In our case, again, because of the extended nature of our representation of the charged particle, there is a potential problem with what amounts to self-interference which needs to be examined. The potential self-interference corrections are always finite, and generally small which is a great advantage over the situation in quantum electrodynamics. 

The difference between the asymptotic forms (3.2) and (3.4) can be traced back the difference in the associated forms of the orbit-orbit interactions mentioned above. Thus we see that in the case of two charged particles the leading asymptotic behavior of V2 depends on the precise definition of Vj,. This observation resolves a longstanding puzzle concerning conflicting results for the value of C2 Further, as was noted some time ago by L. Spruch, 03" is classical in character, i.e. if h and c are restored, Cj turns out to be independent of h. One should therefore try to understand the source of this term from classical electrodynamics. It turns out that this is indeed possible by a reexamination of the work of Darwin [1], but I will not enter into the details here [10]. 

The confirmation by Lamb and Retherford of the inadequacy of the Dirac theory stimulated a re-examination of a theoretical problem to which only a very incomplete solution had so far been found the problem of the interaction between charged particles and the electromagnetic field. We shall briefly refer to the problem as it presented itself in classical physics, and then (following Weisskopf [135]) notice the further difficulties which the quantum theory introduces. Finally we shall see how these difficulties have been circumvented by the new quantum electrodynamics, and how a small correction is thereby introduced to the energy levels predicted by Dirac s theory. The new theory, however, is not a complete and logically satisfactory solution to the problems we shall state a difficulty of principle remains now, as formerly. 

We shall stress here another aspect in favor of PT. Actually in both non-relativistic and relativistic quantum mechanics one studies the motion (mechanics) of charged particles, that interact according to the laws of electrodynamics. The marriage of non-relativistic mechanics with electrodynamics is problematic, since mechanics is Galilei-invariant, but electrodynamics is Lorentz-invariant. Relativistic theory is consistent insofar as both mechanics and electrodynamics are treated as Lorentz-invariant. A consistent non-relativistic theory should be based on a combination of classical mechanics and the Galilei-invariant limit of electrodynamics as studied in subsection 2.9. 

A quantum electrodynamics which demand conservation of the number of charged particles is. .. out of touch with physical reality. . .. It seems that... 

The electric and magnetic polarization fields P(x), M(x) are invoked to describe the electrodynamic properties of charged particles they enter the theory through a representation of the lagrangian interaction potential for a closed system of electric charges and the electromagnetic field... 

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