Is it possible to accommodate massive photons in the framework of a gauge-invariant electrodynamics?

The construction of an alternative electromagnetic theory that preserves Lorentz and gauge symmetries, is considered. We start off by building up Maxwell electrodynamics in (3+1)D from the assumption that the associated Lagrangian is a gauge-invariant functional that depends on the electron and photon fields and their first derivatives only. In this scenario, as well-known, it is not possible to set up a Lorentz invariant gauge theory containing a massive photon. We show nevertheless that there exist two radically different electrodynamics, namely, the Chern-Simons and the Podolsky formulations, in which this problem can be overcome. The former is only valid in odd space-time dimensions, while the latter requires the presence of higher-order derivatives of the gauge field in the Lagrangian. This theory, usually known as Podolsky electrodynamics, is simultaneously gauge and Lorentz invariant; in addition, it contains a massive photon. Therefore, a massive photon, unlike the popular belief, can be adequately accommodated within the context of a gauge-invariant electrodynamics.Comment: 10 page

Calcium Triplet Synthesis

We present theoretical equivalent widths for the sum of the two strongest lines of the Calcium Triplet, CaT index, in the near-IR, using evolutionary techniques and the most recent models and observational data for this feature in individual stars. We compute the CaT index for Single Stellar Populations (instantaneous burst, standard Salpeter-type IMF) at four metallicities, Z=0.004, 0.008, 0.02 (solar) and 0.05, and ranging in age from very young bursts of star formation (few Myr) to old stellar populations, up to 17 gyr, representative of globular clusters, elliptical galaxies and bulges of spirals. The interpretation of the observed equivalent widths of CaT in different stellar systems is discussed. Composite-population models are also computed as a tool to interpret the CaT detections in star-forming regions, in order to disantangle between the component due to Red Supergiants stars, RSG, and the underlying, older, population. CaT is found to be an excellent metallicity-indicator for populations older than 1 Gyr, practically independent of the age. We discuss its application to remove the age- metallicity degeneracy, characteristic of all studies of galaxy evolution based on the usual integrated indices (both broad band colors and narrow band indices). The application of the models computed here to the analysis of a sample of elliptical galaxies will be discussed in a forthcoming paper (Gorgas et al. 1998).Comment: 17 pages, 7 figures, to be published in A&

Topologically stable gapped state in a layered superconductor

We show that a layered superconductor, described by a two-component order parameter, has a gapped state above the ground state, topologically protected from decay, containing flow and counter flow in the absence of an applied magnetic field. This state is made of skyrmions, breaks time reversal symmetry and produces a weak local magnetic field below the present threshold of detection by $\mu$SR and NMR/NQR. We estimate the density of carriers that condense into the pseudogap.Comment: 6 pages, 4 figure