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Covariant Hamiltonian for the electromagnetic two-body problem.
1Universidade 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
Chaos (Woodbury, N.Y.)
|October 29, 2005
Summary
We developed a Hamiltonian formalism for the electromagnetic two-body problem, enabling semiclassical quantization of this foundational electrodynamics model. This approach avoids series expansions for a closed-form solution.
Area of Science:
- Theoretical Physics
- Classical Electrodynamics
- Quantum Mechanics
Background:
- The electromagnetic two-body problem, rooted in action-at-a-distance electrodynamics, has been a subject of study for a century.
- Wheeler and Feynman proposed quantizing this system in the 1940s to address divergences in perturbative Quantum Electrodynamics (QED).
Purpose of the Study:
- To establish a Hamiltonian formalism for the delay equations of motion in the electromagnetic two-body problem.
- To apply this formalism to construct a semiclassical canonical quantization for the attractive interaction case.
Main Methods:
- Developed a finite-dimensional, implicit Hamiltonian that is closed and does not rely on series expansions.
- Utilized numerical trajectories from the attractive electromagnetic two-body problem to inform the quantization process.
Main Results:
- A closed-form Hamiltonian formalism for the electromagnetic two-body problem with arbitrary masses and interactions (repulsive or attractive).
- Successful construction of a semiclassical canonical quantization based on the derived Hamiltonian and numerical solutions.
Conclusions:
- The developed Hamiltonian formalism provides a robust framework for studying the electromagnetic two-body problem.
- This work offers a pathway towards quantizing a historically significant classical electrodynamics system, potentially overcoming limitations of perturbative QED.