On the Observables Describing a Quantum Reference Frame

A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure (POVM) on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure

Reef fishes of Saba Bank, Netherlands Antilles : Assemblage structure across a gradient of habitat types

Saba Bank is a 2,200 km2 submerged carbonate platform in the northeastern Caribbean Sea off Saba Island, Netherlands Antilles. The presence of reef-like geomorphic features and significant shelf edge coral development on Saba Bank have led to the conclusion that it is an actively growing, though wholly submerged, coral reef atoll. However, little information exists on the composition of benthic communities or associated reef fish assemblages of Saba Bank. We selected a 40 km2 area of the bank for an exploratory study. Habitat and reef fish assemblages were investigated in five shallow-water benthic habitat types that form a gradient from Saba Bank shelf edge to lagoon. Significant coral cover was restricted to fore reef habitat (average cover 11.5%) and outer reef flat habitat (2.4%) and declined to near zero in habitats of the central lagoon zone. Macroalgae dominated benthic cover in all habitats (average cover: 32.5 – 48.1%) but dominant algal genera differed among habitats. A total of 97 fish species were recorded. The composition of Saba Bank fish assemblages differed among habitat types. Highest fish density and diversity occurred in the outer reef flat, fore reef and inner reef flat habitats. Biomass estimates for commercially valued species in the reef zone (fore reef and reef flat habitats) ranged between 52 and 83 g/m2. The composition of Saba Bank fish assemblages reflects the absence of important nursery habitats, as well as the effects of past fishing. The relatively high abundance of large predatory fish (i.e. groupers and sharks), which is generally considered an indicator of good ecosystem health for tropical reef systems, shows that an intact trophic network is still present on Saba Bank