Almost Circular Orbits in Classical Action-at-a-Distance Electrodynamics

Andersen, C. M.; Baeyer, Hans Christian von

doi:10.1103/physrevd.5.802

Cited by 34 publications

(32 citation statements)

References 16 publications

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“…This result agrees with that found from a Fokker action principle (Schild 1963, Andersen and von Baeyer 1971, Bruhns 1973. Moreover, Dorling (1970) obtained this result for Dirac's theory of the hydrogen atom.…”

Section: I Isupporting

confidence: 88%

“…The classical electrodynamics of this simple system continues to be a topic for discussion; restricting attention to circular motion (as opposed to one-dimensional motion), much of the literature can be traced from papers by Schild (1963), Schild andSchlosser (1965,1968), Staruszkiewicz (1968), Synge (1972), Andersen andvon Baeyer (1972), Bruhns (1973), Schild (1975Schild ( , 1976, Fahnline (1977), Kracklauer (1978), Stephas (1978 and Fujigaki and Kojima (1978).…”

Section: ] V ( Q )mentioning

confidence: 99%

“…The circumstances under which the result (81) obtains have been examined by Andersen and von Baeyer (1971), and see also Dorling (1970). So long as we have V = 2rF with F = yp2mc2/r, it is clear that 2ymc2+ V = 2(1 -p2) lI2mc .…”

Section: Hence (74) Becomesmentioning

confidence: 99%

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Igor' Ekhiel'evich Dzyaloshinskiĭ (on his sixtieth birthday)

Andreev¹,

Borovik-Romanov²,

Brazovskii³

et al. 1992

Sov. Phys. Usp.

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It is argued that the field of a charge in a stationary orbit co-rotates with the charge about the centre of mass. Such a field has no radiation term. It is obtained by transformation from the co-rotating frame of reference; direct calculation would require that the constitutional properties of the medium be known, these being such as to curve light rays. For rotating reference system Corum's tetrad field is employed, the object of anholonomity affecting the derivation of fields from potentials. The force between the charge *e of positronium is found to be (1 -p2)'/' e 2 / r i 2 when the charges follow with velocity o x r (= pc) a stationary circular orbit of diameter r12 (= 2r).Stationary orbits are selected by Bohr quantisation of canonical angular momentum. A quadratic equation is obtained for yp and for r12, where y = (1 -p2)-1/2. One solution gives the well-known 'atom-like' states. The other gives 'particle-like' states for which orbital motion is ultrarelativistic ( y p = n / a , where a = 1/137), orbital diameters are small compared with e Z / m c 2 ( z d ) , m being the electron mass, and energies are 2amc2/n, small compared with mc2. In such a state positronium is termed a 'positronium unit'. The unit has a very long lifetime for radiative transitions, and should possess a weak magnetic moment ( p " = cued/2n). If it is assigned half-integral orbital angular momentum (hence imaginary parity) it might be identified with the neutrino.A system in which two units orbit around a stationary charge has the properties of the muon, and a system with one orbiting unit has the properties of the charged pion. Spin, charge, rest energy and decay mode are explained in each case. The very different reactivities also can be explained. A system, 'trionium', in which two charges of one sign orbit about a central stationary charge of the opposite sign is explored. Again ultrarelativistic states emerge, but the energies differ inappreciably from the rest energy mc2 of the central charge. However, if one adds further pairs of charges in orbits of increasing radius, the magnetic coupling between orbital currents provides energies of order mc2/a. It is speculated that such a system may afford a model for the proton.

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Section: I Isupporting

confidence: 88%

Section: ] V ( Q )mentioning

confidence: 99%

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Igor' Ekhiel'evich Dzyaloshinskiĭ (on his sixtieth birthday)

Andreev¹,

Borovik-Romanov²,

Brazovskii³

et al. 1992

Sov. Phys. Usp.

View full text Add to dashboard Cite

show abstract

“…Once we are trying to avoid delay equations, it is desirable that the Euler-Lagrange Eqs. for (10) and (11) be ordinary differential equations, which is the heuristic guide for choosing the functional G. A functional G that leaves the two separate problems (10) and (11) in the local form is henceforth called a bilocal ghost Lagrangian G. Here we consider symmetric and time-reversible solutions of Eq. (1) only, but for the variational calculus that follows, it is necessary to study such an orbit immersed in a family of orbits, defined as follows: A time-reversible orbit naturally defines a preferred frame; the Lorentz frame where the orbit is time-reversible, and we henceforth call it the center of mass frame (CMF).…”

Section: Outline Of the Methodsmentioning

confidence: 99%

“…[9] and later rediscovered in Ref. [10] ( see also [11] and [12]). Our problem has already been studied: the symmetric motion of two electrons along a straight line [−x 2 (t) = x 1 (t) ≡ x(t)], which has the following equation in the action-at-a-distance electrodynamics …”

Section: Introductionmentioning

confidence: 99%

Two-degree-of-freedom Hamiltonian for the time-symmetric two-body problem of the relativistic action-at-a-distance electrodynamics

Hollander

Luca

2003

Phys. Rev. E

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We find a two-degree-of-freedom Hamiltonian for the time-symmetric problem of straight line motion of two electrons in direct relativistic interaction. This time-symmetric dynamical system appeared 100 years ago and it was popularized in the 1940's by the work of Wheeler and Feynman in electrodynamics, which was left incomplete due to the lack of a Hamiltonian description. The form of our Hamiltonian is such that the action of a Lorentz transformation is explicitly described by a canonical transformation (with rescaling of the evolution parameter). The method is closed and defines the Hamitonian in implicit form without power expansions. We outline the method with an emphasis on the physics of this complex conservative dynamical system. The Hamiltonian orbits are calculated numerically at low energies using a self-consistent steepest-descent method (a stable numerical method that chooses only the nonrunaway solution). The two-degree-of-freedom Hamiltonian suggests a simple prescription for the canonical quantization of the relativistic twobody problem.

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The Rest-Frame Darwin Potential from the Lienard–Wiechert Solution in the Radiation Gauge

Crater¹,

Lusanna²

2001

Annals of Physics

184

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In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables (Q 2 i = 0, Q i Q j = 0), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of order Q 2 i . By working in the restframe instant form of dynamics, the elimination of the electromagnetic degrees of freedom by means of suitable second classs contraints leads to the identification of the Lienard-Wiechert reduced phase space containing only N charged particles with mutual action-at-a-distance vector and scalar potentials. A Darboux canonical basis of the reduced phase space is found. This allows one to re-express the potentials for arbitrary N as a unique effective scalar potential containing the Coulomb potential and the complete Darwin one, whose 1/c 2 component agrees with the known expression. The effective potential gives the classical analogue of all static and non-static effects of the one-photon exchange Feynman diagram of scalar electrodynamics. C

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Almost Circular Orbits in Classical Action-at-a-Distance Electrodynamics

Cited by 34 publications

References 16 publications

Igor' Ekhiel'evich Dzyaloshinskiĭ (on his sixtieth birthday)

Igor' Ekhiel'evich Dzyaloshinskiĭ (on his sixtieth birthday)

Two-degree-of-freedom Hamiltonian for the time-symmetric two-body problem of the relativistic action-at-a-distance electrodynamics

The Rest-Frame Darwin Potential from the Lienard–Wiechert Solution in the Radiation Gauge

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