Three-dimensional singletons

The three-dimensional analog of singleton gauge theory turns out to be related to the topological gauge theory of Schwartz and Witten. It is a fully-fledged gauge theory, though it involves only a single scalar field. Real, physical degrees of freedom propagate in 3-space, but they are confined in the sense that they cannot be detected locally. The physical Hamiltonian density is not zero, but it is concentrated on the boundary at spatial infinity. This boundary surface, a torus, supports a two-dimensional conformal field theory.     

A general class of (essentially) iso-spectral perturbations

We consider (essentially) iso-spectral perturbations of operators of the formH _A=A ^* A withA being a densely defined closed linear operator from a Hilbert space to another Hilbert space . We perturbH _A by perturbingA asA+B withB being a linear operator from to . Two classes ofB are defined so as to obtain (essentially) iso-spectral perturbations ofH _A. The abstract results are applied to Schrödinger operators. Our approach gives also a mathematical unification for the so-called factorization method in quantum mechanics.     

Central extensions and semi-infinite wedge representations of Krichever-Novikov algebras for more than two points

For the generalized Krichever-Novikov algebras of meromorphic vector fields and their induced modules of weight a different basis is given. With respect to this basis the module structure is generalized graded. Local central extensions of these algebras and their representations on the space of semi-infinite wedge product of forms of weight are studied. In this generalization, one again obtains c = -2(6² -6 +1) as the value for the central charge.     

Unitarizable scalar multipoles

We show that the scalar multipole (81/xxlarge9633.gif" alt="squ" align="MIDDLE" BORDER="0"> +m ²) ⁿ 81/xxlarge966.gif" alt="phgr" align="MIDDLE" BORDER="0"> = 0 forn odd and all massesm81/xxlarge10878.gif" alt="ges" align="MIDDLE" BORDER="0">0 allows a Gupta-Bleuler-type quantization with a unitary space of physical states.Feodor-Lynen fellow of the Humboldt foundation. On leave from Institut für Theoretische Physik, TU Clausthal, Leibnizstr. 10, D3392 Clausthal-Zellerfeld, W. Germany.     

Crystallization features of silicon layers on thermo-insulated substrates under nanosecond laser radiation

P-Si layers on c-Si substrate with a thermo-insulating coating (TIC) were irradiated by the 50-ns second harmonic of an Nd-glass laser. Time-resolved measurements, optical microscopy (OM) and scanning electron microscopy (SEM) data for samples with a 0.1–0.9 m p-Si layer and a 0.1 m SiO₂ or 0.16 m Si₃N₄ TIC layer show that if the p-Si layers melt throughout the depth the solidification starts from the surface as well as from the rear. The latent heat released upon coarse grain growth from the rear prevents further crystallization near the top surface and results in partial or complete remelting of the solid phase on the surface.     

An analysis of the partition of the molecular space in the SCF-MS-Xα method: Calculations of the valence ionization potentials of SiH3F and SiH2F2

Multiple scattering X81j4w553/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> calculations were performed to compute the valence ionization potentials of SiH₃F and SiH₂F₂, with the aim to investigate the effect of different geometrical parameters. The results show that the ordering of the valence levels does not depend on the choice of these parameters, so that MS-X81j4w553/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> calculation may be confidently used in assigning photoelectron spectra.     

VDF（81）／TeFE（19）共聚物的低温低频介电弛豫

用经过改进的介电弛豫谱仪测得不同结晶度的铁电共聚物ＶＤＦ（８１）／ＴｅＦＥ（１９）在－１２０－４０℃、１０－２－１０４ＨＺ范围内的复介电常数．低温介电弛豫过程显示室温以下共聚物的频率谱由低频和高频两部分叠合而成．低频部分符合ＷＬＦ方程，由非晶区被冻结分子链段的微布朗运动贡献；高频部分遵从Ａｒｒｈｅｎｉｕｓ规律，由晶区和非晶区分子链段较小尺度的局域运动产生．结果说明共聚物的玻璃化转变温度是－５２℃，局域弛豫活化能为３７．７ｋＪ／ｍｏｌ．     

Minimal affinizations of representations of quantum groups: the irregular case

Let be a finite-dimensional complex simple Lie algebra and U_q( ) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of U_q( ), an affinization ofV is an irreducible representationVV of the quantum affine algebra U_q( ) which containsV with multiplicity one and is such that all other irreducible U_q( )-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of U_q( ) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if is of typeA, B, C, F orG, the minimal affinization is unique up to U_q( )-isomorphism; (ii) if is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of , there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if U_q( ) is of typeD ₄ and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if is of typeA _n,every affinization is isomorphic to a tensor product of representations of U_q( ) which are irreducible under U_q( ) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701.     

Bundle of quantizations of a symplectic torus

For a given symplectic torus (M=V/,) we construct a bundle whose base is the space of complex structures onV, and whose fibres are the corresponding quantizations ofM. We prove that there is no trivializations of this bundle which allow us to define a continuous identification of the quantizations.     

Fermionic quantum stochastic flows

Existence, uniqueness and, using a higher-order Fermionic Itô formula, multiplicativity are proved for even quantum stochastic flows over ₂graded C ^*-algebras driven by Fermionic noise with bounded structure maps.Work supported by EU HCM Contract CHRX-CT93-QO94.