No abstract

Massive two-flavor QED 2 is known to have many similarities to the two-flavor QCD 4 . Here we compare the π − π scattering amplitudes (actually an analog process in QED 2 ) of the two theories. The QED 2 amplitude is computed from the bosonized version of the model while the QCD 4 amplitude is computed from an effective low energy chiral Lagrangian. A number of interesting features are noted. For example, the contribution of the two-dimensional Wess-Zumino-Witten (WZW) term in QED 2 is structurally identical to the vector meson exchange contribution in QCD 4 . Also it is shown that the QED 2 amplitude computed at tree level is a reasonable approximation to the known exact strong coupling solution. 11.10. Kk, 11.30.Rd, 13.75.Lb

The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed and then specialized to various possible forms for an electromagnetic constitutive law, namely, uniform linear, non-uniform linear, and uniform nonlinear. It is shown that in the uniform linear case, one has four possible ways of prolonging the symmetry Lie algebra, including prolongation to a Lie algebra of infinitesimal projective transformations of a real four-dimensional projective space. In the most general non-uniform linear case, the effect of non-uniformity on symmetry seems inconclusive in the absence of further specifics, and in the uniform nonlinear case, the overall difference from the uniform linear case amounts to a deformation of the electromagnetic constitutive tensor by the electromagnetic field strengths, which induces a corresponding deformation of the symmetry Lie algebra that was obtained in the linear uniform case.

The basic concepts of the formulation of Maxwellian electromagnetism in the absence of a Minkowski scalar product on spacetime are summarized, with particular emphasis on the way that the electromagnetic constitutive law on the space of bivectors over spacetime supplants the role of the Minkowski scalar product on spacetime itself. The complex geometry of the space of bivectors is also summarized, with the intent of showing how an isomorphic copy of the Lorentz group appears in that context. The use of complex 3-spinors to represent electromagnetic fields is then discussed, as well as the expansion of scope that the more general complex projective geometry of the space of bivectors suggests.

It is shown that the pre-metric approach to Maxwell's equations provides an alternative to the traditional EinsteinMaxwell unification problem, namely, that electromagnetism and gravitation are unified in a different way that makes the gravitational field a consequence of the electromagnetic constitutive properties of spacetime, by way of the dispersion law for the propagation of electromagnetic waves.