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Minimizers with discontinuous velocities for the electromagnetic variational method.
1Departamento de Física Rodovia Washington Luis, Universidade Federal de São Carlos, São Paulo 13565-905, Brazil. deluca@df.ufscar.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
Solutions to the electromagnetic two-body problem may have discontinuous derivatives. This study shows that Wheeler-Feynman electrodynamics allows for these discontinuous trajectories, offering a generalized approach to electromagnetic fields and orbits.
Area of Science:
- Electromagnetic theory
- Classical mechanics
- Differential equations
Background:
- The electromagnetic two-body problem involves neutral differential delay equations.
- Solutions with discontinuous derivatives are possible with generic boundary data.
- Wheeler-Feynman electrodynamics is explored for its variational method.
Purpose of the Study:
- To investigate solutions with discontinuous derivatives in the electromagnetic two-body problem.
- To analyze the implications of discontinuous trajectories within Wheeler-Feynman electrodynamics.
- To generalize electromagnetic fields and formulate a generalized absorber hypothesis.
Main Methods:
- Utilizing a boundary value variational method for Wheeler-Feynman electrodynamics.
- Applying Liénard-Wierchert formulas to piecewise defined minimizers.
- Solving a neutral differential delay equation for far fields of localized orbits.
Main Results:
- Minimizer trajectories with discontinuous derivatives are expected in the variational method.
- Generalized electromagnetic fields are defined almost everywhere.
- Localized orbits with vanishing far fields necessitate discontinuous velocities.
Conclusions:
- The study confirms the expectation of discontinuous derivatives in Wheeler-Feynman electrodynamics.
- A generalized absorber hypothesis is formulated, suggesting far fields vanish asymptotically.
- The physics of discontinuous orbits is discussed, highlighting differences from classical mechanics and introducing a spinorial four-current.
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