Covariant Hamiltonian for the electromagnetic two-body problem.
We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.
De Luca
Jayme
J
Universidade Federal de São Carlos, Departamento de Física, Rodovia Washington Luis, km 235 Caixa Postal 676, São Carlos, São Paulo 13565-905, Brazil. deluca@df.ufscar.br
D000465:Algorithms; D003198:Computer Simulation; D004574:Electromagnetic Fields; D008956:Models, Chemical; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013314:Stress, Mechanical