11
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Exact solutions of the bound Dirac and Klein Gordon equations in non co propagating electromagnetic plane waves

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          A new class of exact solutions of the bound Dirac and bound Klein Gordon equations in non co propagating plane waves is found. The solutions are based on the physical principle of maintaining local gauge invariance in the Furry picture Lagrangian when N external fields can undergo independent gauge transformations. The solutions can be expressed in terms of the Hamilton Jacobi action and a gauge invariant effective particle momentum in the ensemble of external fields. Rotations of the effective particle momentum, which preserve local gauge invariance, are introduced into the action using matrix calculus. The set of such rotations provides the class of new solutions constituting a family of Volkov like solutions for one external field. When applied to two or more non co propagating external fields, the rotational symmetry provides counter terms which decouple the fields. The bound state equations of motion become solvable for any number of non co propagating external fields. Through angular spectral decomposition, which represents electromagnetic fields of any form as a spatial Fourier series of non co propagating plane waves, the new solutions described here can be applied to strong field physics problems in any external electromagnetic field.

          Related collections

          Most cited references17

          • Record: found
          • Abstract: not found
          • Article: not found

          �ber eine Klasse von L�sungen der Diracschen Gleichung

          D. Wolkow (1935)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            On Bound States and Scattering in Positron Theory

            W. Furry (1951)
              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Fundamental processes of quantum electrodynamics in laser fields of relativistic power

                Bookmark

                Author and article information

                Journal
                16 July 2018
                Article
                1808.01238
                ead5bfea-116f-48cd-b858-db56a9de35d3

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                8 pages
                physics.optics hep-ph hep-th

                High energy & Particle physics,Optical materials & Optics
                High energy & Particle physics, Optical materials & Optics

                Comments

                Comment on this article