Abelian 3-form gauge theory: superfield approach

We discuss a D-dimensional Abelian 3-form gauge theory within the framework of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for this theory. To pay our homage to Victor I. Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form (antisymmetric tensor) gauge field, we go a step further and discuss the above D-dimensional Abelian 3-form gauge theory within the framework of BRST formalism and establish that the existence of the (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow Region, Russi

Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.Comment: 11 pages, Latex (minor changes, to appear in Lett.Math.Phys.

Nilpotent (anti-)BRST symmetry transformations for dynamical non-Abelian 2-form gauge theory: superfield formalism

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the dynamical non-Abelian 2-form gauge theory within the framework of geometrical superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian densities that respect the above nilpotent symmetry transformations. We discuss, furthermore, this (anti-) BRST invariance in the language of the superfield formalism. One of the novel features of our investigation is the observation that, in addition to the horizontality condition, we have to invoke some other physically relevant restrictions to deduce the exact (anti-) BRST symmetry transformations for all the fields of the topologically massive non-Abelian gauge theory.Comment: LaTeX file, 8 pages, typos fixed in some equations, journal-versio

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ

Bi-photon propagation control with optimized wavefront by means of Adaptive Optics

We present an efficient method to control the spatial modes of entangled photons produced through SPDC process. Bi-photon beam propagation is controlled by a deformable mirror, that shapes a 404nm CW diode laser pump interacting with a nonlinear BBO type-I crystal. Thanks to adaptive optical system, the propagation of 808nm SPDC light produced is optimized over a distance of 2m. The whole system optimization is carried out by a feedback between deformable mirror action and entangled photon coincidence counts. We also demonstrated the improvement of the two-photon coupling into single mode fibers

The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated WW algebra

For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV hierarchy). The $W$--algebra associated to the \shs\, of the $(n,m)$--th KdV hierarchy (called $W(n,m)$ algebra) is isomorphic via a Miura map to the direct sum of $W_m$--algebra, $W_{n+m}$--algebra and an additional $U(1)$ current algebra. In turn, from the latter, we can always construct a representation of $W_\infty$--algebra.Comment: 26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43, revised version with addition

Notoph Gauge Theory: Superfield Formalism

We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the "notoph" (i.e. the opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticommutativity of the (anti-) BRST transformations and their resolution within the framework of geometrical superfield approach to BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely anticommutative in nature.Comment: LaTeX file, 12 pages, Talk delivered at SQS'09 (BLTP, JINR, Dubna

Corago in LOD. The debut of an Opera repository into the Linked Data arena

The paper examines the adoption of the Semantic Web (SW) technologies and Linked Data (LD) principles to manage a knowledge base about opera. The Corago repository collects historical data and documentation about opera works, performances and librettos from the 16th to the 20th century. We experimented the use of semantic technologies to manage the repository’s knowledge catalogued following the Functional Requirements for Bibliographic Records (FRBR) relational model. Cultural Heritage Knowledge Bases (CHKB) as Corago could leverage SW and LD to overcome proprietary models and to introduce new information to better satisfy user’s requirements. Two well-established reference ontologies as CIDOC Conceptual Reference Model (CIDOC CRM) and FRBR Object Oriented (FRBRoo) are adopted to transpose contents form the legacy conceptual model to RDF. Through the process, we observed that formal semantics allow, not only to adequately represent the opera domain, but also enable to define the way information is being presented to users. This led to the definition of “reception pathways” which become themselves part of the knowledge about opera within the KB. This novel semantic approach is introduced with the Corago Semantic Model (Corago SM), a domain ontology dedicated to functional representation of opera’s historical data. Advancements have been tested with an experimental system and assessed through a questionnaire submitted to a panel of users

RePIM in LOD: semantic technologies to manage, preserve, and disseminate knowledge about Italian secular music and lyric poetry from the 16th-17th centuries

Il progetto RePIM in LOD si è posto l’obiettivo di pubblicare il "Repertorio della Poesia Italiana in Musica, 1500-1700" (RePIM) come dataset Linked Open Data (LOD). Per l'ampiezza e il dettaglio dei suoi contenuti, il RePIM è un archivio di riferimento per la ricerca sulla musica profana italiana dei secoli XVI-XVII. Negli ultimi anni, gli studiosi hanno potuto accedervi attraverso un'applicazione web realizzata nei primi anni Duemila. A causa dell'obsolescenza della sua piattaforma informatica, l'archivio RePIM era destinato a essere messo offline. Per preservare questa preziosa fonte, il progetto ha migrato i suoi contenuti in una base di conoscenza adottando tecnologie semantiche e progettando un'applicazione aggiornata per l'utente finale. L'articolo illustra le problematiche poste dalla gestione delle informazioni sulla tradizione madrigalistica e della conservazione digitale delle informazioni bibliografiche e filologiche nel campo della musica profana italiana e della poesia lirica dei secoli XVI-XVII.The RePIM in LOD project aimed to publish the "Repertorio della Poesia Italiana in Musica, 1500-1700" (RePIM) as Linked Open Data (LOD) dataset. For the extent and detail of its contents, RePIM is a reference archive for research on Italian secular music from the 16th-17th centuries. In recent years, scholars have been able to access it through a public web-based application. Due to the obsolescence of its information technology platform, the RePIM repository was set to be taken offline. To preserve this precious source, the project migrated its contents into a knowledge base adopting semantic technologies and designing an up-to-date enduser application. The article illustrates the challenges of managing information about madrigal tradition and the digital knowledge preservation of bibliographic and philological information in the field of Italian secular music and lyric poetry of the 16th-17th centuries