Exotic solutions in string theory

Klimenko, Stanislav; Nikitin, Igor

doi:10.1007/bf03036006

Cited by 12 publications

(20 citation statements)

References 10 publications

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“…Thus, as a relativistic AaD-counterpart of the shortrange interquark interaction, the Wheeler-Feynman elec-trodynamics [39,40] is appropriate. The corresponding two-body problem is described by the Fokker action (2.1), (2.2), and is a lifelong subject of study [59,60,[70][71][72][73][74]. In particular, a circular orbit dynamics is defined by the following equations and integrals of motion [59,60]:…”

Section: Accounting a One-gluon Exchange Interactionmentioning

confidence: 99%

Regge trajectories in the framework of the relativistic action-at-a-distance theory

Duviryak¹

2015

J. Phys. Stud.

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A relativistic quark model of mesons formulated within the formalism of Fokker-type action integrals is proposed, in which an interquark interaction is mediated by a massless vector field and scalar-vector superposition of higher derivative fields. In the non-relativistic limit the model describes a two-particle system with the Cornell potential. In order to analyze the model in the essentially relativistic domain the perturbed circular orbit approximation is applied which permits one to perform the canonical quantization of the model. It is shown that the model reproduces well specific features of the light meson spectroscopy.

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Section: Accounting a One-gluon Exchange Interactionmentioning

confidence: 99%

Regge trajectories in the framework of the relativistic action-at-a-distance theory

Duviryak¹

2015

J. Phys. Stud.

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“…In the present Poincaré-invariant case, besides a time transformation and use of the energy constant, it is further necessary to define special finite variables to accomplish manifest regularization. The non-local expression for the conserved energy of the electromagnetic two-body problem [1,22,23] is therefore used here in two ways:…”

Section: The Equations Of Motionmentioning

confidence: 99%

“…The conserved energy of the Kepler problem is simple and well known, while the corresponding energy for our relativistic problem is somewhat unfamiliar. The Poincaré invariance of the Fokker Lagrangian determines a four-vector constant of motion, which involves an integral over a light-cone of the orbit [1,22,23]. For the one-dimensional symmetric motion of equal masses, as explained in Ref.…”

Section: Two Finite Variables Defined By the Energymentioning

confidence: 99%

“…For the one-dimensional symmetric motion of equal masses, as explained in Ref. [23], the total energy…”

Section: Two Finite Variables Defined By the Energymentioning

confidence: 99%

“…where r + , v + 2 and r − , v − 2 stand for the radius and velocity at the advanced and retarded lightcones of particle 1 respectively, as illustrated in Figure 4. The total linear momentum of a symmetric orbit can also be expressed as P W F T = P 1 + P 2 = 0 [23], with the time-reversed pair of constants P 1 and P 2 given by…”

Section: Two Finite Variables Defined By the Energymentioning

confidence: 99%

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Regularization of the collision in the electromagnetic two-body problem

Hollander

Luca

2004

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. We use the energy constant related to the Poincare invariance of the theory to define finite variables with finite derivatives at the collision. The collision orbits are calculated numerically using the regular equation adapted in a self-consistent minimization method (a stable numerical method that chooses only nonrunaway solutions). This dynamical system appeared 100 years ago as an example of covariant time-symmetric two-body dynamics and acquired the status of electrodynamics in the 1940s by the works of Dirac, Wheeler, and Feynman. We outline the method with an emphasis on the physics of this complex conservative dynamical system.

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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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Exotic solutions in string theory

Cited by 12 publications

References 10 publications

Regge trajectories in the framework of the relativistic action-at-a-distance theory

Regge trajectories in the framework of the relativistic action-at-a-distance theory

Regularization of the collision in the electromagnetic two-body problem

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

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