Is there action-at-a-distance linear confinement?

Abstract

The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system J. Math. Phys. 53, 083703 (2012) ECE-imaging of the H-mode pedestal (invited) Rev. Sci. Instrum. 83, 10E329 (2012) The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories J. Math. Phys. 53, 072903 (2012) Operator extensions theory model for electromagnetic field-electron interactionThe possilibity of constructing an action-at-a-distance form of linear confinement is demonstrated. Using the Fokker-Wheeler-Feynman action principle, known from classical action-at-a-distance electrodynamics, with an action containing the relativistically invariant twoparticle Heaviside step function, equations of motion and appropriate potentials exhibiting the linearity of their behavior are derived. The plausibility of the generators of motion describing dynamics with the linear potentials is verified on the simple circular-orbit model of a twocomponent system, and the expected energy spectrum in terms of semiclassical quantization is obtained.

Contact interactions between particle worldlines

“…In this way T interpolates between the classical field associated to a pair of charges and a regime in which field lines are concentrated about the line joining the charges. The emergence of confining behaviour has briefly been considered for action at a distance theories before [42,43] and we add to the discussion with our determination of the field lines with this new model. The three dimensional plot in Fig.…”

Fokker-Type Confinement Models From Effective Lagrangian in Classical Yang–mills Theory

“…Up to the numerical factor, the only difference between (19) and (21) is that the function δ(x 2 ) is replaced by Θ(x 2 ). This substitution was guessed by Weiss in Ref.…”

“…26 For NT it corresponds to the action-at-a distance confinement model in the form by Weiss. 21 The Rivacoba's form of this action integral 20 follows from (39).…”

Quantization of almost-circular orbits in the Fokker action formalism

“…Of physical interest is a study, in ACO approximation, of various Fokker-type systems, especially those which may have relevance to the relativistic bound state problems in the nuclear and hadronic physics. In particular, some Fokker-type systems with confining interaction may serve as relativistic potential model of mesons [15][16][17][18]. Thereupon the quantization procedure of Fokker-type models which is based on ACO approximation scheme should be developed.…”

“…16) where S(t) and u are defined in (2.5),(3.6), and symmetry properties (4.4)-(4.5), (4.8)-(4.9),(4.11)-(4.14) one can define "tilded" Fokkerians: L a (ẋ a ) = L a (S a u a ) = L a (u a ) ≡L a (z a ,ż a ; Ω), (4.17)…”