How to add a boundary condition

Given a conformal QFT local net of von Neumann algebras B_2 on the two-dimensional Minkowski spacetime with irreducible subnet A\otimes\A, where A is a completely rational net on the left/right light-ray, we show how to consistently add a boundary to B_2: we provide a procedure to construct a Boundary CFT net B of von Neumann algebras on the half-plane x>0, associated with A, and locally isomorphic to B_2. All such locally isomorphic Boundary CFT nets arise in this way. There are only finitely many locally isomorphic Boundary CFT nets and we get them all together. In essence, we show how to directly redefine the C* representation of the restriction of B_2 to the half-plane by means of subfactors and local conformal nets of von Neumann algebras on S^1.Comment: 20 page

A Remark on Quantum Group Actions and Nuclearity

Let H be a compact quantum group with faithful Haar measure and bounded counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if its fixed-point subalgebra is nuclear. As a consequence H is a nuclear C*-algebra.Comment: 12 pages, LateX 2

La routine

La pratica dell\u2019insegnamento dovrebbe scaturire sempre da una riflessione sulla pratica stessa, dovrebbe tradursi in un \u201cfare riflessivo\u201d, cio\ue8 in un \u201cfare\u201d pi\uf9 consapevole; infatti il racconto della propria esperienza e la riflessione sulle proprie pratiche permette di essere pi\uf9 consapevoli di ci\uf2 che viene fatto, del come viene fatto e del perch\ue9. Tutto ci\uf2 permette all\u2019insegnante di decentrarsi dall\u2019azione, di analizzarla e di sviluppare la capacit\ue0 di analisi delle situazioni educativo-didattiche. La narrazione attraverso la routine, risulta fondamentale per sviluppare la riflessione metacognitiva e per rintracciare la motivazione profonda che spinge l\u2019insegnante ad operare determinate scelte: innesca momenti di riflessione e di metacognizione sulle strategie educative e didattiche attivate dentro le situazioni. L\u2019insegnante riflette sulla \u201csituazione d\u2019apprendimento\u201d esperita, coglie gli aspetti problematici e non, discute sulla validit\ue0 del metodo e rielabora criticamente l\u2019esperienza vissuta prendendo consapevolezza delle competenze acquisite durante il processo attivato. Il lavoro di narrazione delle routine pu\uf2 produrre effetti formativi, sulla consapevolezza dei partecipanti rispetto alla propria crescita personale e alle competenze acquisite, aspetti che possono indubbiamente risultare particolarmente rilevanti per lo sviluppo professionale

Some computations in the cyclic permutations of completely rational nets

In this paper we calculate certain chiral quantities from the cyclic permutation orbifold of a general completely rational net. We determine the fusion of a fundamental soliton, and by suitably modified arguments of A. Coste , T. Gannon and especially P. Bantay to our setting we are able to prove a number of arithmetic properties including congruence subgroup properties for $S, T$ matrices of a completely rational net defined by K.-H. Rehren .Comment: 30 Pages Late

Evidence of a pressure-induced metallization process in monoclinic VO2_2

Raman and combined trasmission and reflectivity mid infrared measurements have been carried out on monoclinic VO$_2$ at room temperature over the 0-19 GPa and 0-14 GPa pressure ranges, respectively. The pressure dependence obtained for both lattice dynamics and optical gap shows a remarkable stability of the system up to P*$\sim$10 GPa. Evidence of subtle modifications of V ion arrangements within the monoclinic lattice together with the onset of a metallization process via band gap filling are observed for P$>$P*. Differently from ambient pressure, where the VO$_2$ metal phase is found only in conjunction with the rutile structure above 340 K, a new room temperature metallic phase coupled to a monoclinic structure appears accessible in the high pressure regime, thus opening to new important queries on the physics of VO$_2$.Comment: 5 pages, 3 figure