327 research outputs found
Infinitesimal deformation quantization of complex analytic spaces
Global constructions of quantization deformation and obstructions are
discussed for an arbitrary complex analytic space in terms of adapted
(analytic) Hochschild cohomology. For K3-surfaces an explicit global
construction of a Poisson bracket is given. It is shown that the analytic
Hochschild (co)homology on a complex space has structure of coherent analytic
sheaf in each degree
Deformation quantization of cosmological models
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is
applied to cosmological models in the minisuperspace. The quantization
procedure is performed explicitly for quantum cosmology in a flat
minisuperspace. The de Sitter cosmological model is worked out in detail and
the computation of the Wigner functions for the Hartle-Hawking, Vilenkin and
Linde wave functions are done numerically. The Wigner function is analytically
calculated for the Kantowski-Sachs model in (non)commutative quantum cosmology
and for string cosmology with dilaton exponential potential. Finally, baby
universes solutions are described in this context and the Wigner function is
obtained.Comment: 37 pages, 16 figure
Traces for star products on the dual of a Lie algebra
In this paper, we describe all traces for the BCH star-product on the dual of
a Lie algebra. First we show by an elementary argument that the BCH as well as
the Kontsevich star-product are strongly closed if and only if the Lie algebra
is unimodular. In a next step we show that the traces of the BCH star-product
are given by the \ad-invariant functionals. Particular examples are the
integration over coadjoint orbits. We show that for a compact Lie group and a
regular orbit one can even achieve that this integration becomes a positive
trace functional. In this case we explicitly describe the corresponding GNS
representation. Finally we discuss how invariant deformations on a group can be
used to induce deformations of spaces where the group acts on.Comment: 18 pages, LaTeX2e. Updated reference
The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization
Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf
algebra of renormalization in perturbative quantum field theory, we investigate
the relation between the twisted antipode axiom in that formalism, the Birkhoff
algebraic decomposition and the universal formula of Kontsevich for quantum
deformation.Comment: 21 pages, 15 figure
Measurement of air and nitrogen fluorescence light yields induced by electron beam for UHECR experiments
Most of the Ultra High Energy Cosmic Ray (UHECR) experiments and projects
(HiRes, AUGER, TA, EUSO, TUS,...) use air fluorescence to detect and measure
extensive air showers (EAS). The precise knowledge of the Fluorescence Light
Yield (FLY) is of paramount importance for the reconstruction of UHECR. The
MACFLY - Measurement of Air Cherenkov and Fluorescence Light Yield - experiment
has been designed to perform such FLY measurements. In this paper we will
present the results of FLY in the 290-440 nm wavelength range for dry air and
pure nitrogen, both excited by electrons with energy of 1.5 MeV, 20 GeV and 50
GeV. The experiment uses a 90Sr radioactive source for low energy measurement
and a CERN SPS electron beam for high energy. We find that the FLY is
proportional to the deposited energy (E_d) in the gas and we show that the air
fluorescence properties remain constant independently of the electron energy.
At the reference point: atmospheric dry air at 1013 hPa and 23C, the ratio
FLY/E_d=17.6 photon/MeV with a systematic error of 13.2%.Comment: 19 pages, 8 figures. Accepted for publication in Astroparticle
Physic
Linear-response theory and lattice dynamics: a muffin-tin orbital approach
A detailed description of a method for calculating static linear-response
functions in the problem of lattice dynamics is presented. The method is based
on density functional theory and it uses linear muffin-tin orbitals as a basis
for representing first-order corrections to the one-electron wave functions. As
an application we calculate phonon dispersions in Si and NbC and find good
agreement with experiments.Comment: 18 pages, Revtex, 2 ps figures, uuencoded, gzip'ed, tar'ed fil
Noncommutativity from spectral flow
We investigate the transition from second to first order systems. This
transforms configuration space into phase space and hence introduces
noncommutativity in the former. Quantum mechanically, the transition may be
described in terms of spectral flow. Gaps in the energy or mass spectrum may
become large which effectively truncates the available state space. Using both
operator and path integral languages we explicitly discuss examples in quantum
mechanics, (light-front) quantum field theory and string theory.Comment: 31 pages, one Postscript figur
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