Gauge fields associated with the manifestly covariant dynamics of particles in (3, 1) spacetime are five-dimensional. We provide solutions of the classical 5D gauge field equations in both (4, 1) and (3, 2) flat spacetime metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.

In this paper we explore the problem of fields generated by a source undergoing hyperbolic motion in the framework of Stueckelberg manifestly covariant relativistic dynamics. The resulting gauge fields are computed numerically using Green-Functions which are retarded in the Stueckelberg absolute time τ, and qualitatively compared with Maxwell fields generated by the same motion. The gauge invariant field equations are second order in this parameter as well as in space-time, resulting in identification of a five-dimensional manifold for the gauge fields. We find that although the zero mode of all fields coincides with the corresponding Maxwell fields, the generalized Lorentz force (necessarily involving a fifth component of the gauge field) depends on the nonzero modes as well, which affects the motion of particles subject to these forces.

Offshell electrodynamics based on a manifestly covariant off-shell relativistic dynamics of Stueckelberg, Horwitz, and Piron, is five-dimensional. In this paper, we study the problem of radiation reaction of a particle in motion in this framework. In particular, the case of above-mass-shell is studied in detail, where the renormalization of the Lorentz force leads to a system of non-linear differential equations for 3 Lorentz scalars. The system is then solved numerically, where it is shown that the mass-shell deviation scalar ε either smoothly falls down to 0 (this result provides a mechanism for the mass stability of the off-shell theory), or strongly diverges under more extreme conditions. In both cases, no runaway motion is observed. Stability analysis indicates that the system seems to have chaotic behavior. It is also shown that, although a motion under which the mass-shell deviation ε is constant but not-zero, is indeed possible, but, it is unstable, and eventually it either decays to 0 or diverges. C 2012 American Institute of Physics. [http://dx.

We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analogue of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network—a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focussing in particular on the effect of frustration of the dissipative coupling. We theoretically analyse the dynamics using coupled nonlinear Mathieu’s equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings.

In previous papers derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter τ ). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable τ .