Covariant Hamiltonian for the electromagnetic two-body problem

Journal Article · Thu Sep 01 00:00:00 EDT 2005 · Chaos (Woodbury, N. Y.)

DOI:https://doi.org/10.1063/1.1999567· OSTI ID:20692942

Luca, Jayme de ^[1]

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1. Universidade Federal de Sao Carlos, Departamento de Fisica, Rodovia Washington Luis, km 235 Caixa Postal 676, Sao Carlos, Sao Paulo 13565-905 (Brazil)

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.

• OSTI ID: 20692942
• Journal Information: Chaos (Woodbury, N. Y.), Vol. 15, Issue 3; Other Information: DOI: 10.1063/1.1999567; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ELECTROMAGNETISM
EQUATIONS OF MOTION
HAMILTONIANS
MASS
PERTURBATION THEORY
QUANTIZATION
QUANTUM ELECTRODYNAMICS
SEMICLASSICAL APPROXIMATION
SERIES EXPANSION
TRAJECTORIES
TWO-BODY PROBLEM