Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1)

The group Diff(S^1) of the orientation preserving diffeomorphisms of the circle S^1 plays an important role in conformal field theory. We consider a subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity". This subgroup is of interest for the actual physical theory living on the punctured circle, or the real line. We investigate the unique central extension K of the Lie algebra of that group. We determine the first and second cohomologies, its ideal structure and the automorphism group. We define a generalization of Verma modules and determine when these representations are irreducible. Its endomorphism semigroup is investigated and some unitary representations of the group which do not extend to Diff(S^1) are constructed.Comment: 34 pages, no figur

Detection of highly ionized O and Ne absorption lines in the X-ray spectrum of 4U1820-303 in the globular cluster, NGC 6624

We searched for absorption lines of highly ionized O and Ne in the energy spectra of two Low-mass X-ray binaries, 4U1820-303 in the globular cluster NGC6624 and Cyg X-2, observed with the Chandra LETG, and detected O VII, O VIII and Ne IX absorption lines for 4U1820-303. The equivalent width of the O VII K alpha line was 1.19 +0.47/-0.30 eV (90 % errors) and the significance was 6.5 sigma. Absorption lines were not detected for Cyg X-2 with a 90 % upper limit on the equivalent width of 1.06 eV for O VII K alpha. The absorption lines observed in 4U1820-303 are likely due to hot interstellar medium, because O will be fully photo-ionized if the absorbing column is located close to the binary system. The velocity dispersion is restricted to b = 200 - 420 km/s from consistency between O VII K alpha and K beta lines, Ne/O abundance ratio, and H column density. The average temperature and the O VII density are respectively estimated to be log(T[K]) = 6.2 - 6.3 and n(OVII) = (0.7 - 2.3) x 10^{-6} cm^{-3}. The difference of O VII column densities for the two sources may be connected to the enhancement of the soft X-ray background (SXB) towards the Galactic bulge region. Using the polytrope model of hot gas to account for the SXB we corrected for the density gradient and estimated the midplane O VII density at the solar neighborhood. The scale height of hot gas is then estimated using the AGN absorption lines. It is suggested that a significant portion of both the AGN absorption lines and the high-latitude SXB emission lines can be explained by the hot gas in our Galaxy.Comment: Accepted for publication in ApJ. 7 pages, 9 eps figure

Datta-Das type spin-field effect transistor in non-ballistic regime

It is revealed that in spin helix state of (001) quantum well system, strong suppression of D'yakonov-Perel' spin relaxation process occurs by an interplay between Rashba and Dresselhaus couplings over a wide range of Rashba coupling strength. Contrary to common belief in early works, this leads to the finding that Datta-Das type spin-field effect transistor is actually applicable to more realistic non-ballistic transport regime in two dimensional electron gas system.Comment: 8 pages, 3 figure

Neural crest stem cells undergo multilineage differentiation in developing peripheral nerves to generate endoneurial fibroblasts in addition to Schwann cells

Neural crest stem cells (NCSCs) persist in peripheral nerves throughout late gestation but their function is unknown. Current models of nerve development only consider the generation of Schwann cells from neural crest, but the presence of NCSCs raises the possibility of multilineage differentiation. We performed Cre-recombinase fate mapping to determine which nerve cells are neural crest derived. Endoneurial fibroblasts, in addition to myelinating and non-myelinating Schwann cells, were neural crest derived, whereas perineurial cells, pericytes and endothelial cells were not. This identified endoneurial fibroblasts as a novel neural crest derivative, and demonstrated that trunk neural crest does give rise to fibroblasts in vivo, consistent with previous studies of trunk NCSCs in culture. The multilineage differentiation of NCSCs into glial and non-glial derivatives in the developing nerve appears to be regulated by neuregulin, notch ligands, and bone morphogenic proteins, as these factors are expressed in the developing nerve, and cause nerve NCSCs to generate Schwann cells and fibroblasts, but not neurons, in culture. Nerve development is thus more complex than was previously thought, involving NCSC self-renewal, lineage commitment and multilineage differentiation

Asymptotic completeness in a class of massless relativistic quantum field theories

This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.Comment: 15 pages, LaTeX. As appeared in Communications in Mathematical Physic