Pre-metric electromagnetism as a path to unification

It is shown that the pre-metric approach to Maxwell's equations provides an alternative to the traditional Einstein-Maxwell unification program, namely, that electromagnetism and gravitation are unified in a different way that makes the gravitational field a consequence of the electromagnetic constitute properties of spacetime, by way of the dispersion law for the propagation of electromagnetic waves.Comment: 7 pages. Paper submitted to the IX Symposium honoring noted French mathematical physicist Jean-Pierre Vigier at Morgan State University, November 16-19, 2014. Appearing in conference proceedings: Unified Field Mechanics, eds. R. L. Amoroso, L. H. Kaufmann, P. Rowlands, World Scientific, New Jersey, 201

Remark on the Potential Function of the Linear Sigma Model

It is shown that the potential functions for the ordinary linear sigma model can be divided into two topographically different types depending on whether the quantity $R\equiv(m_\sigma/m_\pi)^2$ is greater than or less than nine. Since the Wigner-Weyl mode (R=1) and the Nambu-Goldstone mode ($R=\infty$ belong to different regions, we speculate that this classification may provide a generalization to the broken symmetry situation, which could be convenient for roughly characterizing different possible applications of the model. It is noted that a more complicated potential does not so much change this picture as add different new regions.Comment: 26 pages, 11 figures (gzipped