594 research outputs found
Gravity, Non-Commutative Geometry and the Wodzicki Residue
We derive an action for gravity in the framework of non-commutative geometry
by using the Wodzicki residue. We prove that for a Dirac operator on an
dimensional compact Riemannian manifold with , even, the Wodzicki
residue Res is the integral of the second coefficient of the heat
kernel expansion of . We use this result to derive a gravity action for
commutative geometry which is the usual Einstein Hilbert action and we also
apply our results to a non-commutative extension which, is given by the tensor
product of the algebra of smooth functions on a manifold and a finite
dimensional matrix algebra. In this case we obtain gravity with a cosmological
constant.Comment: 17p., MZ-TH/93-3
Discotic materials for organic electronics
Discotic Materials for Electronic Applications Marcel Kastler The modulation of the pronounced aggregation propensity of alkyl substituted hexa-perihexabenzocoronenes (HBCs, Figure 1) has been achieved by a reduction of the intermolecular attractive forces. Sterically demanding branched, racemic alkyl chains, with the branching site in close proximity to the aromatic core, have been introduced in a synthetically straight forward fashion. A striking feature is the ability to melt these novel HBCs with the bulkiest side chains at temperatures, which are below the thermal decomposition threshold. This opened the possibility to apply cheap melt-processing, such as zone-crystallization to obtain uniaxially organized molecules over macroscopical areas. Depending on the steric demand excerted by the side-chain, different molecular orientations with respect to the support have been achieved, which is very important for the successful implementation in devices, which require different orientations of the charge carrier pathways. Another important prerequisite for the implementation of materials into organic electronic devices is a high charge carrier mobility to allow an unperturbed migration of free charge carriers in the device structure. Time-resolved pulse-radiolysis microwave conductivity (TR-PRMC) and time-of-flight (TOF) measurements revealed good charge carrier mobilities for the novel materials together with very long charge carrier life-times. Implemented in organic heterojunction photovoltaics, good performing devices were obtained. The variation of the polycyclic aromatic hydrocarbon (PAH) perimeter has been theoretically predicted to influence strongly the electronic properties. Going from the âall-arm chairâ HBC to PAHs with one, two and three âzigzagâ sites (Figure ), the electronic spectroscopy revealed pronounced differences between the derivatives. However, the symmetry and the size of the aromatic core component in these derivatives excerted a strong influence onto molecular properties, such as the number of transitions in the UV/vis spectrum. The tuning of the electronic levels of materials is a fundamental task in material science to optimize the injection of charge carriers from electrodes with a specific work function. HBC Figure 1: âzigzagâ PAHs. Finally, the supramolecular order revealed a dependence upon the substitution pattern of the alkyl chains attached in the corona of the PAHs. Higher symmetry substitution patterns with fewer chains stabilized the intracolumnar organization, due to a better crystallization. In summary, next to the synthesis of new materials holding promise for organic electronics, novel concepts have been developed which allow a simpler functionalization of the PAH based discotic materials both in the periphery and at the aromatic core. This functionalization permits a fine-tuning of molecular and supramolecular properties, which is important to obtain promising materials for the application in organic electronic devices. Diskotische Materialien fĂŒr elektronische Anwendungen Marcel Kastler Die Kontrolle der ausgeprĂ€gten AggregationsfĂ€higkeit von alkylsubstituierten Hexa-perihexabenzocoronenen (HBC) wurde durch die Reduktion der intermolekularen Wechselwirkungen erreicht. Sterisch anspruchsvolle, verzweigte Alkylketten, mit einem Verzweigungspunkt naher des aromatischen Kerns, wurden in die Corona der aromatischen Scheiben eingebracht und verleihen den Derivaten Schmelzbarkeit ohne thermische Zersetzung. Dies erlaubte eine kostengĂŒnstige Verarbeitungstechniken direkt aus der Schmelze wie z.B. Zonenschmelzen, um uniaxial organisierte makroskopische Filme zu erhalten. AbhĂ€ngig von dem sterischen Anspruch, der durch die Seitenkette erzeugt wird, wurden unterschiedliche molekulare Orientierungen auf OberflĂ€chen erhalten, was eine wichtige Voraussetzung ist, um diskotische Materialien in elektronische Bauteile zu implementieren. Eine weitere Voraussetzung sind hohe LadungstrĂ€gerbeweglichkeiten und LadungstrĂ€gerlebenszeiten in den Halbleitermaterialien, die mit time-resolved pulseradiolysis microwave conductivity (TR-PRMC) und time-of-flight (TOF) auch fĂŒr die synthetisieren Materialien bestimmt wurden. Die neuen Materialien zeigten bereits in organischen Solarzellen gute Leistungen. Den Einfluss des Perimeters auf die elektronischen Eigenschaften der polyzyklischen aromatischen Kohlenwasserstoffe (PAKs) wurde theoretisch vorhergesagt und in dieser Arbeit durch die Synthese einer homologe Serie von PAKs experimentell bestĂ€tigt. Geht man von der âarm-chairâ Peripherie des HBC sukzessive zu einer partiellen âzickzackâ Peripherie, so findet man eine AbhĂ€ngigkeit der elektronischen Banden von Symmetrie und GröĂe des aromatischen Systems. Die spontan ausgebildete Ăberstruktur dieser Derivate zeigte eine AbhĂ€ngigkeit von Substitutionsmuster und der Natur der Alkylketten. Zusammenfassend wurden neben der Synthese von neuartigen Materialien fĂŒr den Einsatz in der organischen Elektronik Synthesen entwickelt, die eine vereinfachte Funktionalisierung von ausgedehnten PAKs ermöglicht. Diese Konzepte erlauben eine Justierung der molekularen und supramolekularen Eigenschaften, eines der wichtigsten Voraussetzungen fĂŒr den Einsatz von Materialien in elektronischen Bauelementen
Fluctuation Operators and Spontaneous Symmetry Breaking
We develop an alternative approach to this field, which was to a large extent
developed by Verbeure et al. It is meant to complement their approach, which is
largely based on a non-commutative central limit theorem and coordinate space
estimates. In contrast to that we deal directly with the limits of -point
truncated correlation functions and show that they typically vanish for provided that the respective scaling exponents of the fluctuation
observables are appropriately chosen. This direct approach is greatly
simplified by the introduction of a smooth version of spatial averaging, which
has a much nicer scaling behavior and the systematic developement of Fourier
space and energy-momentum spectral methods. We both analyze the regime of
normal fluctuations, the various regimes of poor clustering and the case of
spontaneous symmetry breaking or Goldstone phenomenon.Comment: 30 pages, Latex, a more detailed discussion in section 7 as to
possible scaling behavior of l-point function
Non-Commutative Geometry and Chiral Perturbation Lagrangian
Chiral perturbation lagrangian in the framework of non-commutative geometry
is considered in full detail. It is found that the explicit symmetry breaking
terms appear and some relations between the coupling constants of the theory
come out naturally. The WZW term also turns up on the same footing as the other
terms of the chiral lagrangian.Comment: Latex, 9 page
Quantum electrodynamics of relativistic bound states with cutoffs
We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing
the interaction of relativistic electrons and positrons in the Coulomb
potential with photons in Coulomb gauge. The interaction includes both
interaction of the current density with transversal photons and the Coulomb
interaction of charge density with itself. We prove that the Hamiltonian is
self-adjoint and has a ground state for sufficiently small coupling constants.Comment: To appear in "Journal of Hyperbolic Differential Equation
Gravity coupled with matter and foundation of non-commutative geometry
We first exhibit in the commutative case the simple algebraic relations
between the algebra of functions on a manifold and its infinitesimal length
element . Its unitary representations correspond to Riemannian metrics and
Spin structure while is the Dirac propagator ds = \ts \!\!---\!\! \ts =
D^{-1} where is the Dirac operator. We extend these simple relations to
the non commutative case using Tomita's involution . We then write a
spectral action, the trace of a function of the length element in Planck units,
which when applied to the non commutative geometry of the Standard Model will
be shown (in a joint work with Ali Chamseddine) to give the SM Lagrangian
coupled to gravity. The internal fluctuations of the non commutative geometry
are trivial in the commutative case but yield the full bosonic sector of SM
with all correct quantum numbers in the slightly non commutative case. The
group of local gauge transformations appears spontaneously as a normal subgroup
of the diffeomorphism group.Comment: 30 pages, Plain Te
The uses of Connes and Kreimer's algebraic formulation of renormalization theory
We show how, modulo the distinction between the antipode and the "twisted" or
"renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes
the proofs of equivalence of the (corrected) Dyson-Salam,
Bogoliubov-Parasiuk-Hepp and Zimmermann procedures for renormalizing Feynman
amplitudes. We discuss the outlook for a parallel simplification of
computations in quantum field theory, stemming from the same algebraic
approach.Comment: 15 pages, Latex. Minor changes, typos fixed, 2 references adde
Study of Interplanetary Magnetic Field with Ground State Alignment
We demonstrate a new way of studying interplanetary magnetic field -- Ground
State Alignment (GSA). Instead of sending thousands of space probes, GSA allows
magnetic mapping with any ground telescope facilities equipped with
spectropolarimeter. The polarization of spectral lines that are pumped by the
anisotropic radiation from the Sun is influenced by the magnetic realignment,
which happens for magnetic field (<1G). As a result, the linear polarization
becomes an excellent tracer of the embedded magnetic field. The method is
illustrated by our synthetic observations of the Jupiter's Io and comet Halley.
Polarization at each point was constructed according to the local magnetic
field detected by spacecrafts. Both spatial and temporal variations of
turbulent magnetic field can be traced with this technique as well. The
influence of magnetic field on the polarization of scattered light is discussed
in detail. For remote regions like the IBEX ribbons discovered at the boundary
of interstellar medium, GSA provides a unique diagnostics of magnetic field.Comment: 11 pages, 19 figures, published in Astrophysics and Space Scienc
Differential Algebras in Non-Commutative Geometry
We discuss the differential algebras used in Connes' approach to Yang-Mills
theories with spontaneous symmetry breaking. These differential algebras
generated by algebras of the form functions matrix are shown to be
skew tensorproducts of differential forms with a specific matrix algebra. For
that we derive a general formula for differential algebras based on tensor
products of algebras. The result is used to characterize differential algebras
which appear in models with one symmetry breaking scale.Comment: 21 page
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