16779871
Deformed W N Algebras from Elliptic Sl(n ) Algebras
We extend to the sl(N) case the results that we previously obtained on the construction of W q,p algebras from the elliptic algebra A q,p (sl(2) c). The elliptic algebra A q,p (sl(N) c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N (N − 1)/2 integers, defining q-deformations of the W N algebra, are constructed. The operators t(z) also close an exchange algebra when (−p 1 2) N M = q −c−N for M ∈ Z. It becomes Abelian when in addition p = q N h where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W N algebras depending on the parity of h, characterizing the exchange structures at p = q N h as new W q,p (sl(N)) algebras. Résumé Nousétendons au cas sl(N) les résultats que nous avons obtenus précédemment concernant la construction des algèbres W q,p ` a partir de l'algèbre elliptique A q,p (sl(2) c). L'algèbre elliptique A q,p (sl(N) c) au niveau critique c = −N possède un centré etendu contenant des opérateurs de trace t(z). On construit sur ce centre des familles de structures de Poisson indicées par N (N − 1)/2 entiers, définissant des q-déformations de l'algèbre W N. Les opérateurs t(z) engendrent une algèbre d'´ echange lorsque (−p 1 2) N M = q −c−N o` u M ∈ Z. Cette algèbre devient abélienne si de plus p = q N h avec h entier non nul. Les structures de Poisson obtenues dans ces limites classiques contiennent différentes algèbres W N q-déformées dépendant de la parité de l'entier h, caractérisant les structures d'´ echangè a p = q N h comme de nouvelles algèbres W q,p (sl(N)).
120458416
Unitary group representations in fock spaces with generalized exchange properties
We investigate the notion of secondR-quantization - a suitable deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics. We also perform theR-quantization of a class of unitary one-particle representations relevant for the description of symmetries. The Euclidean covariance of anyons is analyzed within this context.
9495374
CENTRAL EXTENSIONS OF CLASSICAL AND QUANTUM Q-VIRASORO ALGEBRAS
We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra Aq,p(sl(N))c. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the literature.
18478779
A braided Yang–Baxter algebra in a theory of two coupled lattice quantum KdV: algebraic properties and ABA representations
A generalization of the Yang–Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang–Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of algebraic Bethe ansatz techniques. The conjecture that this monodromy matrix algebra leads, in the cylinder continuum limit, to a perturbed minimal conformal field theory description is analysed and supported.
120678958
Fock representations of exchange algebras with involution
An associative algebra AR with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in AR and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov–Faddeev algebra is also explored.
119389503
Hubbard's adventures in Script N = 4 SYM-land? Some non-perturbative considerations on finite length operators
As the Hubbard energy at half-filling is believed to reproduce at strong coupling (part of) the all loop expansion of the dimensions in the SU(2) sector of the planar = 4 SYM (super-Yang–Mills theory), we compute an exact non-perturbative expression for it. With this aim, we use the effective and well-known idea in 2D statistical field theory of converting the Bethe ansatz equations into two coupled non-linear integral equations (NLIEs). We focus our attention on the highest anomalous dimension for fixed bare dimension or length, L, analysing the many advantages of this method for extracting exact behaviours on varying the length and the' t Hooft coupling, λ. For instance, we will show that the large L (asymptotic) expansion is exactly reproduced by its analogue in the Beisert–Dippel–Staudacher (BDS) Bethe ansatz, though the exact expression clearly differs from the BDS one (in having non-analytic terms). Taking the limits on L and λ in different orders is also under strict control. Eventually, the precision of numerical integration of the NLIEs is as impressive as in other easier-looking theories.
122836697
CVD diamond films as photon detectors
Abstract We present an overview of our research on Chemical Vapour Deposited (CVD) diamond films as photon detectors. Samples are grown in our laboratories using three different methods: microwave plasma enhanced CVD (MWPECVD), DC glow discharge CVD (DCGDCVD) and hot filament CVD (HFCVD). We present the photoelectrical properties of these samples having contacts in planar and sandwich configuration, taking into account the roles of material microstructure and electrical configuration. Their photoresponse has been measured in the whole visible–near UV spectral range with the aim to characterize their UV selectivity and to evaluate their gap-state density.