Book Description

Abstract. The non-linear electromagnetic theory proposed by Dr. Schiff is investigated. Nbn-Maxwellian plane wave solutions of the field equations, k = - (l + A^) A^ , are obtained. Static, particlelike solutions of the field equations are considered in the absence of a magnetic field. Existence of well behaved solutions, in the case of spherical symmetry, is formally established. The list of known spherically symmetric, neutral and charged particlelike solutions is extended to include "compound" solutions which correspond to an imaginary vector potential in certain (linear) regions of space. Sufficient conditions are derived under which variational approximations yield upper bounds to the Lagrangian associated with the class of field equations Ad = F'(d) . The usual parameter variation method is generalised, in the case of more than one dimension, to admit variation of functions of one of the independent variables. This method is used to obtain approximations to possible nonspherical, odd parity, neutral particlelike eigensolutions of Ad = d - d^. The results, however, seem to give an approximation to the lowest two-particle state rather than a one-particle state of odd parity. A variational principle for charged particlelike solutions is developed and used to obtain approximations to the lowest (in energy) spherically symmetric state. A scheme is suggested whereby integral relations, which are satisfied by integrable solutions of Ad = F T (d), may be generated. The first few such integral relations are derived and are used, in the particular case F'(t) - 4> - t J , to obtain alternate expressions for the energy, / [^-( Vt)"+ F(t) ]d of the system and to test variational approximations to the solutions of the field equation. The dynamical stability of neutral particlelike solutions, against certain dissociation modes, is demonstrated; in particular, against direct dissociation into plane waves and into particles for which ...