Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

Scalar glueballs: Constraints from the decays into η or η′

We study the mixing of the scalar glueball into the isosinglet mesons f0(1370), f0(1500), and f0(1710) to describe the two-body decays to pseudoscalars. We use an effective Hamiltonian and employ the two-angle mixing scheme for η and η′. In this framework, we analyze existing data and look forward to new data into η and η′ channels. For now, the f0(1710) has the largest glueball component and a sizable branching ratio into ηη′, testable at BESIII.

Absolute line intensities for formic acid and dissociation constant of the dimer

Absolute line intensities in the v6 and v8 interacting bands of trans-HCOOH, observed near 1105.4 and 1033.5 cm -1, respectively, and the dissociation constant of the formic acid dimer (HCOOH)2 have been measured using Fourier transform spectroscopy at a resolution of 0.002 cm-1. Eleven spectra of formic acid, at 296.0(5) K and pressures ranging from 14.28(25) to 314.0(24) Pa, have been recorded between 600 and 1900 cm-1 with an absorption path length of 19.7(2) cm. 437 integrated absorption coefficients have been measured for 72 lines in the v6 band. Analysis of the pressure dependence yielded the dissociation constant of the formic acid dimer, k p=361(45) Pa, and the absolute intensity of the 72 lines of HCOOH. The accuracy of these results was carefully estimated. The absolute intensities of four lines of the weak v8 band were also measured. Using an appropriate theory, the integrated intensity of the v6 and v 8 bands was determined to be 3.47 × 1017 and 4.68 × 10-19 cm-1/(molecule cm-1) respectively, at 296 K. Both the dissociation constant and integrated intensities were compared to earlier measurements. © 2007 American Institute of Physics.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.