Quantum Theory in Accelerated Frames of Reference

The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac's equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.Comment: 25 pages, no figures, contribution to Springer Lecture Notes in Physics (Proc. SR 2005, Potsdam, Germany, February 13 - 18, 2005

Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces

We study the existence and shape preserving properties of a generalized Bernstein operator B n fixing a strictly positive function f 0 , and a second function f 1 such that f 1 /f 0 is strictly increasing, within the framework of extended Chebyshev spaces U n . The first main result gives an inductive criterion for existence: suppose there exists a Bernstein operator B n : C [ a,b ] → U n with strictly increasing nodes, fixing f 0 ,f 1 ∈ U n . If U n ⊂ U n +1 and U n +1 has a non-negative Bernstein basis, then there exists a Bernstein operator B n +1 : C [ a,b ] → U n +1 with strictly increasing nodes, fixing f 0 and f 1 . In particular, if f 0 ,f 1 ,...,f n is a basis of U n such that the linear span of f 0 ,..,f k is an extended Chebyshev space over [ a,b ] for each k = 0 ,...,n , then there exists a Bernstein operator B n with increasing nodes fixing f 0 and f 1 . The second main result says that under the above assumptions the following inequalities hold B n f ≥ B n +1 f ≥ f for all ( f 0 ,f 1 )-convex functions f ∈ C [ a,b ] . Furthermore, B n f is ( f 0 ,f 1 )-convex for all ( f 0 ,f 1 )-convex functions f ∈ C [ a,b ] .AD 26/03/201

Multi-messenger Observations of a Binary Neutron Star Merger

International audienceOn 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\sim 1.7\,{\rm{s}}$ with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg(2) at a luminosity distance of ${40}_{-8}^{+8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 $\,{M}_{\odot }$. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\sim 40\,{\rm{Mpc}}$) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ∼10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position $\sim 9$ and $\sim 16$ days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta