# On Group Invariant Solutions to the Maxwell Dirac equations

Legg, GP 2007 , 'On Group Invariant Solutions to the Maxwell Dirac equations', Research Master thesis, University of Tasmania.

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## Abstract

This work constitutes a study on group invariant solutions of the Maxwell Dirac
equations for a relativistic electron spinor in its own self-consistent electromagnetic field. First, the Maxwell Dirac equations are written in a gauge independent tensor form, in terms of bilinear Dirac currents and a gauge independent
total four-potential. A requirement of this form is that the length of the current
vector be non-zero. In this form they are amenable to the study of solutions invariant under subgroups of the Poincaré group without reference to the Abelian
gauge group. In particular, all subgroups of the Poincaré group that generate 4
dimensional orbits by transitive action on Minkowski space, and the corresponding invariant vector fields are identifed, which will constitute invariant solutions
merely if various constants satisfy a set of algebraic equations. For each such
subgroup, the possibility of solutions to both the full Maxwell Dirac equations
and to a classical approximation to the self-field equations is determined. Of
the 19 classes of simply transitive subgroups, only one class yielded a solution.

Item Type: Thesis - Research Master Legg, GP The Author Copyright 2007 the author View statistics for this item

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