Thermal States in Conformal QFT. II

We continue the analysis of the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on the real line. In the first part we have proved the uniqueness of KMS state on every completely rational net. In this second part, we exhibit several (non-rational) conformal nets which admit continuously many primary KMS states. We give a complete classification of the KMS states on the U(1)-current net and on the Virasoro net Vir_1 with the central charge c=1, whilst for the Virasoro net Vir_c with c>1 we exhibit a (possibly incomplete) list of continuously many primary KMS states. To this end, we provide a variation of the Araki-Haag-Kastler-Takesaki theorem within the locally normal system framework: if there is an inclusion of split nets A in B and A is the fixed point of B w.r.t. a compact gauge group, then any locally normal, primary KMS state on A extends to a locally normal, primary state on B, KMS w.r.t. a perturbed translation. Concerning the non-local case, we show that the free Fermi model admits a unique KMS state.Comment: 36 pages, no figure. Dedicated to Rudolf Haag on the occasion of his 90th birthday. The final version is available under Open Access. This paper contains corrections to the Araki-Haag-Kaster-Takesaki theorem (and to a proof of the same theorem in the book by Bratteli-Robinson). v3: a reference correcte

A 3-component extension of the Camassa-Holm hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of the CH equation.Comment: 15 pages; minor changes; to appear in Letters in Mathematical Physic

Inherited structures in deformations of Poisson pencils

In this paper we study some properties of bi-Hamiltonian deformations of Poisson pencils of hydrodynamic type. More specifically, we are interested in determining those structures of the fully deformed pencils that are inherited through the interaction between structural properties of the dispersionless pencils (in particular exactness or homogeneity) and suitable finiteness conditions on the central invariants (like polynomiality). This approach enables us to gain some information about each term of the deformation to all orders in $\epsilon$. Concretely, we show that deformations of exact Poisson pencils of hydrodynamic type with polynomial central invariants can be put, via a Miura transformation, in a special form, that provides us with a tool to map a fully deformed Poisson pencil with polynomial central invariants of a given degree to a fully deformed Poisson pencil with constant central invariants to all orders in $\epsilon$. In particular, this construction is applied to the so called $r$-KdV-CH hierarchy that encompasses all known examples with non-constant central invariants. As far as homogeneous Poisson pencils of hydrodynamic type is concerned, we prove that they can also be put in a special form, if the central invariants are homogeneous polynomials. Through this we can compute the homogeneity degree about the tensorial component appearing in each order in $\epsilon$, namely the coefficient of the highest order derivative of the $\delta$.Comment: 34 pages. Theorem 5 correcte

La condizione e il contributo delle Chiese nell’Unione europea

Lo studio approfondisce lo status giuridico delle Chiese nel diritto dell'Unione europea a partire dall'inquadramento giuridico e dottrinale del "tema religione" internamente al rapporto tra diritti nazionali e diritto sovranazionale e della sua rinnovata centralità a tutti i livelli e in seguito sviluppa la tematica in relazione alle fonti comunitarie e internazionali e definisce il contributo specifico delle Chiese alle politiche comunitarie nella prospettiva del dialogo "strutturato" dell'art. 17 TFUE

La Menzogna: Le altre facce della realtà

Il volume presenta contributi scientifici sul tema della menzogna nelle sue più diversificate ‘manifestazioni’ testuali e declinazioni ‘comunicative’, potendo essere intesa come immaginazione, invenzione, finzione, artificio, dissimulazione, deformazione ma anche come manipolazione.Il volume si articola in tre macrosezioni: letteraria, filologica-linguistica e artistica. La sezione letteraria contiene una riflessione ramificata che offre uno sguardo multiprospettico. La menzogna è analizzata dapprima come tema per poi tramutarsi in oggetto di studio della critica letteraria, giungendo, infine, in un mutevole paesaggio geoculturale. La seconda sezione, quella filologica-linguistica, segue invece un principio diacronico: si indaga la menzogna a partire dalla tradizione manoscritta fino alla comunicazione digitale. La terza e ultima sezione, che conferma la natura interdisciplinare e transmediale del volume, è dedicata alle strategie di rappresentazione e dissimulazione in rapporto alle diverse forme d’arte, quali il teatro, le serie TV, la docufiction, nonché le arti performative. Il volume si chiude con un’appendice che contiene le riproduzioni delle opere pittoriche di alcuni artisti, presentate in occasione della mostra che ha affiancato la Graduate Conference