Fractional Euler-Lagrange differential equations via Caputo derivatives

We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in pres

The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.Comment: Revtex, 6 pages, 2 figures. v2: Some small corrections. v3: Citation of a earlier paper included. v4: Some stylistic changes. v5: Final version to appear in AJ

The Casimir effect for the scalar and Elko fields in a Lifshitz-like field theory

In this work, we obtain the Casimir energy for the real scalar field and the Elko neutral spinor field in a field theory at a Lifshitz fixed point (LP). We analyze the massless and the massive case for both fields using dimensional regularization. We obtain the Casimir energy in terms of the dimensional parameter and the LP parameter. Particularizing our result, we can recover the usual results without LP parameter in (3+1) dimensions presented in the literature. Moreover, we compute the effects of the LP parameter in the thermal corrections for the massless scalar field.Comment: 20 pages, 2 figures, some results have been modified and other changes to the text have been made to match the accepted version in Eur. Phys. J.

The dust masses of powerful radio galaxies: clues to the triggering of their activity

We use deep Herschel Space Observatory observations of a 90% complete sample of 32 intermediate-redshift 2Jy radio galaxies (0.05 < z < 0.7) to estimate the dust masses of their host galaxies and thereby investigate the triggering mechanisms for their quasar-like AGN. The dust masses derived for the radio galaxies (7.2x10^5 < M_d < 2.6x10^8 M_sun) are intermediate between those of quiescent elliptical galaxies on the one hand, and ultra luminous infrared galaxies (ULIRGs) on the other. Consistent with simple models for the co-evolution of supermassive black holes and their host galaxies, these results suggest that most of the radio galaxies represent the late time re-triggering of AGN activity via mergers between the host giant elliptical galaxies and companion galaxies with relatively low gas masses. However, a minority of the radio galaxies in our sample (~20%) have high, ULIRG-like dust masses, along with evidence for prodigious star formation activity. The latter objects are more likely to have been triggered in major, gas-rich mergers that represent a rapid growth phase for both their host galaxies and their supermassive black holes.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter