Solutions of the Wheeler-Feynman equations with discontinuous velocities

Autor(es)

de Souza, Daniel Camara ^[1] ; De Luca, Jayme ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Fis, Dept Fis Matemat, BR-05508090 Sao Paulo - Brazil

^[2] Univ Fed Sao Carlos, Dept Fis, BR-13565905 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 25, n. 1 JAN 2015.
• Citações Web of Science: 1

Resumo

We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have discontinuous velocities. We construct a numerical method to solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann conditions and calculate some numerical orbits with discontinuous velocities. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space. (C) 2015 Author(s). (AU)

• Processo FAPESP: 11/18343-6 - Eletrodinâmica variacional
• Beneficiário: Jayme Vicente de Luca Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/16964-0 - Eletrodinâmica Variacional e Problema Eletromagnético de Dois e Três Corpos
• Beneficiário: Daniel Câmara de Souza
• Modalidade de apoio: Bolsas no Brasil - Doutorado