## About

40

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Introduction

Additional affiliations

January 2003 - present

**Università degli Studi di Roma "La Sapienza"**

September 1998 - February 2002

Education

September 1989 - May 1997

## Publications

Publications (40)

A base $\Delta$ generating the topology of a space $M$ becomes a partially ordered set (poset), when ordered under inclusion of open subsets. Given a precosheaf over $\Delta$ of fixed-point spaces (typically C*-algebras) under the action of a group $G$, in general one cannot find a precosheaf of $G$-spaces having it as fixed-point precosheaf. Rathe...

Within the framework of the universal algebra of the electromagnetic field, the impact of globally neutral configurations of external charges on the field is analyzed. External charges are not affected by the field, but they induce localized automorphisms of the universal algebra. Gauss's law implies that these automorphisms cannot be implemented b...

Given a Haag-Kastler net on a globally hyperbolic spacetime, one can consider a family of regions where quantum charges are supposed to be localized. Assuming that the net fulfills certain minimal properties (factoriality of the global observable algebra and relative Haag duality), we give a geometric criterion that the given family must fulfill to...

We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting factor"). If the twisting factor is fundamental solution of a differential operator, then applying the differential operator to the bosonic field yields a gen...

Let A be a C*-algebra, h a Hilbert space and C h the CAR algebra over h. We construct a twisted tensor product of A by C h such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be regarded as a generalized CAR algebra constructed over a suitable Hilbert A-bimodule. As an application,...

Within the framework of the universal algebra of the electromagnetic field, the impact of globally neutral configurations of external charges on the field is analyzed. External charges are not affected by the field, but they induce localized automorphisms of the universal algebra. Gauss’s law implies that these automorphisms cannot be implemented b...

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss’ law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of t...

We show that the Aharonov-Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labeling cha...

A recent idea, put forward by Mund, Rehren and Schroer, is discussed; it suggests that in gauge quantum field theory, one can replace the point-localized gauge fields by string-localized vector potentials built from gauge-invariant observables and a principle of string independence. Based on a kinematical model, describing unmovable (static) fields...

A recent idea, put forward by Mund, Rehren and Schroer, is discussed; it suggests that in gauge quantum field theory one can replace the point-localized gauge fields by string-localized vector potentials built from gauge invariant observables and a principle of
string-independence. Based on a kinematical model, describing unmovable (static) fields...

The basic aspects of the Aharonov-Bohm effect can be summarized by the remark that wavefunctions become sections of a line bundle with a flat connection (that is, a "flat potential"). Passing at the level of quantum field theory in curved spacetimes, we study the Dirac field interacting with a classical (background) flat potential and show that it...

Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge invariant) vector potentials, integrated about spacelike separated, spatial loops, are elements of the center of th...

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated...

A universal C*-algebra of the electromagnetic field is constructed. It is
represented in any quantum field theory which incorporates electromagnetism and
expresses basic features of this field such as Maxwell's equations, Poincar\'e
covariance and Einstein causality. Moreover, topological properties of the
field resulting from Maxwell's equations a...

A universal C*-algebra of the electromagnetic field is constructed. It is
represented in any quantum field theory which incorporates electromagnetism and
expresses basic features of this field such as Maxwell's equations, Poincar\'e
covariance and Einstein causality. Moreover, topological properties of the
field resulting from Maxwell's equations a...

The present work tackles the existence of local gauge symmetries in the
setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops,
previously introduced by the authors, is a model independent construction of a
covariant net of local C*-algebras on any 4-dimensional globally hyperbolic
spacetime, aimed to capture some structural prop...

Motivated by algebraic quantum field theory, we study presheaves of symmetric tensor categories defined on the base of a space, intended as a spacetime. Any section of a presheaf (that is, any "superselection sector", in the applications that we have in mind) defines a holonomy representation whose
triviality is measured by Cheeger-Chern-Simons cha...

Let X be a space, intended as a possibly curved spacetime, and A a precosheaf
of C*-algebras on X. Motivated by algebraic quantum field theory, we study the
Kasparov and Theta-summable K-homology of A interpreting them in terms of the
holonomy equivariant K-homology of the associated C*-dynamical system. This
yields a characteristic class for K-hom...

We show that superselection structures on curved spacetimes, that are expected to describe quantum charges affected by the underlying geometry, are categories of sections of presheaves of symmetric tensor categories. When an embedding functor is given, the superselection structure is a Tannaka-type dual of a locally constant group bundle, which hen...

Slides of the talk in the conference Noncommutative Geometry and Applications, Mondragone (Frascati), June 2014

Given a connected and locally compact Hausdorff space X with a good base K we
assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A
defined over K. Afterwards we consider the representation theory and the
Kasparov K-homology of A, and interpret them in terms, respectively, of the
representation theory and the K-homology of...

We continue studying net bundles over partially ordered sets (posets),
defined as the analogues of ordinary fibre bundles. To this end, we analyze the
connection between homotopy, net homology and net cohomology of a poset, giving
versions of classical Hurewicz theorems. Focusing our attention on Hilbert net
bundles, we define the K-theory of a pos...

In recent times a new kind of representations has been used to describe
superselection sectors of the observable net over a curved spacetime, taking
into account of the effects of the fundamental group of the spacetime. Using
this notion of representation, we prove that any net of C*-algebras over S^1
admits faithful representations, and when the n...

The present paper deals with the question of representability of nets of C*-algebras whose underlying poset, indexing the net, is not upward directed. A particular class of nets, called C*-net bundles, is classified in terms of C*-dynamical systems having as group the fundamental group of the poset. Any net of C*-algebras has a canonical morphism i...

We provide a model independent construction of a net of C*-algebras
satisfying the Haag-Kastler axioms over any spacetime manifold. Such a net,
called the net of causal loops, is constructed by selecting a suitable base K
encoding causal and symmetry properties of the spacetime. Considering K as a
partially ordered set (poset) with respect to the i...

Lectures notes (in italian) of some arguments of classical analysis, with
exercises. A particular emphasis to functional analysis and elementary operator
algebra theory is given, by means of exercises and examples.

Given a quasi-special endomorphism $\rho$ of a C*-algebra A with nontrivial
center, we study an extension problem for automorphisms of A to a minimal
cross-product B of A by $\rho$. Exploiting some aspects of the underlying
generalized Doplicher-Roberts duality theory based on Pimsner algebras, an
obstruction to the existence of such extensions is...

We give a short proof of the nuclearity property of a class of Cuntz-Pimsner
algebras associated with a Hilbert A-bimodule M, where A is a separable and
nuclear C*-algebra. We assume that the left A-action on the bimodule M is given
in terms of compact module operators and that M is direct summand of the
standard Hilbert module over A.

C*-endomorphisms arising from superselection structures with non-trivial
centre define a 'rank' and a 'first Chern class'. Crossed products by such
endomorphisms involve the Cuntz-Pimsner algebra of a vector bundle having the
above-mentioned rank and first Chern class, and can be used to construct a
duality for abstract (nonsymmetric) tensor catego...

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalises the Dixmier–Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As an application, the duality breaking for group bundles vs. tensor C*-categories with nonsimple unit is discus...

In the present paper we study tensor C*-categories with non-simple unit
realised as C*-dynamical systems (F,G,\beta) with a compact (non-Abelian) group
G and fixed point algebra A := F^G. We consider C*-dynamical systems with
minimal relative commutant of A in F, i.e. A' \cap F = Z, where Z is the center
of A which we assume to be nontrivial. We gi...

In algebraic quantum field theory the spacetime manifold is replaced by a
suitable base for its topology ordered under inclusion. We explain how certain
topological invariants of the manifold can be computed in terms of the base
poset. We develop a theory of connections and curvature for bundles over posets
in search of a formulation of gauge theor...

A duality is discussed for Lie group bundles vs. certain tensor C * -categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C * -algebra bundles with fibre a fixed-point algebra of the Cuntz algebra: a classification is given, and a cohomological invariant is assigned, represen...

We introduce the notion of fibred action of a group bundle on a C(X)-algebra.
By using such a notion, a characterization in terms of induced C*-bundles is
given for C*-dynamical systems such that the relative commutant of the
fixed-point algebra is minimal (i.e., it is generated by the centre of the
given C*-algebra and the centre of the fixed-poin...

We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify...

An overview about C*-algebra bundles with a Z-grading is presented, with
particular emphasis on classification questions. In particular, we discuss the
role of the representable KK(X ; -, -)-bifunctor introduced by Kasparov. As an
application, we consider Cuntz-Pimsner algebras associated with vector bundles,
and give a classification in terms of K...

We study C*-algebra endomorphims which are special in a weaker sense w.r.t.
the notion introduced by Doplicher and Roberts. We assign to such endomorphisms
a geometrical invariant, representing a cohomological obstruction for them to
be special in the usual sense. Moreover, we construct the crossed product of a
C*-algebra by the action of the dual...

We study the Cuntz–Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. Furthermore, we assign to bundles of Cuntz algebras carrying a global circle action a class in the representable KK-group of the zero-grade bundle. We explicitly compute such class for...

We construct the crossed product of a C(X)-algebra by an endomorphism, in
such a way that the endomorphism itself becomes induced by the bimodule of
continuous sections of a vector bundle. Some motivating examples for such a
construction are given. Furthermore, we study the C*-algebra of G-invariant
elements of the Cuntz-Pimsner algebra associated...

The notion of extension of a given C*-category by a C*-algebra A is introduced. In the commutative case A=C(Ω), the objects of the extension category are interpreted as fiber bundles over Ω of objects belonging to the initial category. It is shown that the Doplicher–Roberts algebra (DR-algebra in the following) associated to an object in the extens...