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.

Neurology and psychiatry: waking up to opportunities of sleep. State of the art and clinical/research priorities for the next decade.

In recent years, evidence has emerged for a bidirectional relationship between sleep and neurological and psychiatric disorders. First, sleep-wake disorders (SWDs) are very common and may be the first/main manifestation of underlying neurological and psychiatric disorders. Secondly, SWDs may represent an independent risk factor for neuropsychiatric morbidities. Thirdly, sleep-wake function (SWF) may influence the course and outcome of neurological and psychiatric disorders. This review summarizes the most important research and clinical findings in the fields of neuropsychiatric sleep and circadian research and medicine, and discusses the promise they bear for the next decade. The findings herein summarize discussions conducted in a workshop with 26 European experts in these fields, and formulate specific future priorities for clinical practice and translational research. More generally, the conclusion emerging from this workshop is the recognition of a tremendous opportunity offered by our knowledge of SWF and SWDs that has unfortunately not yet entered as an important key factor in clinical practice, particularly in Europe. Strengthening pre-graduate and postgraduate teaching, creating academic multidisciplinary sleep-wake centres and simplifying diagnostic approaches of SWDs coupled with targeted treatment strategies yield enormous clinical benefits for these diseases.