Quantum BRST charge for quadratically nonlinear Lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {T _a ,T _b }=f _ab ^c T _c +V _ab ^cd T _c T _d , (classical algebras in terms of Poisson brackets) and [T _a ,T _b ]=h _ab I+f _ab ^c T _c +V _ab ^cd (T _c T _d )(quantum algebras in terms of commutator brackets; normal ordering of the product (T _c T _d ) is understood). In both cases we assume that the set of generators {T _a } splits into a set {H _i } generating an ordinary Lie algebra and remaining generators {S }, such that only theV _ij are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=–2(N–3).     

De Sitter superalgebras and supergravity

A general analysis of all possible super-extensions of anti-de Sitter and de Sitter algebrasO(3, 2) andO(4, 1) is presented. It is shown that actions with de Sitter local supersymmetry exist, but contain vector-ghosts.Supported in part by the NSF under grant PHY 81-09110 A-01On leave from the Institute of Theoretical Physics, University of Wrocaw, Wrocaw, Poland     

Competition between glassiness and order in a multispin glass

A mean-field multispin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet, and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.     

Thermodynamic picture of the glassy state gained from exactly solvable models

A picture for thermodynamics of the glassy state was introduced recently by us [Phys. Rev. Lett. 79, 1317 (1997); 80, 5580 (1998)]. It starts by assuming that one extra parameter, the effective temperature, is needed to describe the glassy state. This approach connects responses of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized, nonequilibrium way. Similar universal relations do not hold between energy fluctuations and the specific heat. In the present paper, the underlying arguments are discussed in greater length. The main part of the paper involves details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics. At low temperature, the relaxation time of both models diverges as an Arrhenius law, which causes glassy behavior in typical situations. In the glassy regime, we are able to verify the above-mentioned relations for the thermodynamics of the glassy state. In the course of the analysis, it is argued that stretched exponential behavior is not a fundamental property of the glassy state, though it may be useful for fitting in a limited parameter regime.     

Geometry of coset spaces and massless modes of the squashed seven-sphere in supergravity

We derive some general results for Killing vectors on arbitrary coset manifolds and explicitly exhibit the squashed seven-sphere as the coset space Sp₄×Sp₂/Sp₂×Sp₂. Using these results, we then analyze the zero-mass sector of supergravity of the squashed S⁷ and argue that it is not interpretable as a spontaneously broken version of N=8 supergravity. We also point out the existence of a new solution which combines squashing and torsion.     

A SAW gas sensor for NO2. Chemically immobilized phthalocyanines as chemical interface

Summary A surface acoustic wave (SAW) gas sensor for NO₂ has been developed in which a chemically immobilized copper(II)-phthalocyanine layer was applied using 3-aminopropyl triethoxysilane as a spacer instead of a sublimated layer. The response time is shortened and the sensitivity is decreased in this way. It is expected that response time and selectivity will improve even more when true monolayers are obtained instead of the observed layers containing the polymerized spacer.

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SAW-Gassensor fur NO₂. Chemisch immobilisierte Phthalocyanine als chemisches Interface