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Aknowledgements I am very pleased to have the opportunity here to express my sincere thanks to Professor Bacciotti who has guided me in the study of mathematics for five years, giving me confidence and transmitting his fondness for this discipline. Particular thanks also to Professor Conti. It has been really a pleasure to attend his course in Control… (More)

An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed– point net of the field net under a compact group. This compact group is its canonical gauge group if the occurrence of sectors with infinite statistics… (More)

- Paolo Bertozzini, Roberto Conti, Roberto Longo
- 1998

Let A be a local conformal net of von Neumann algebras on S and ρ a Möbius covariant representation of A, possibly with infinite dimension. If ρ has finite index, ρ has automatically positive energy. If ρ has infinite index, we show the spectrum of the energy always to contain the positive real line, but, as seen by an example, it may contain negative… (More)

We classify Haag-dual Poincaré covariant subsystems B ⊂ F of a graded-local net F on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net FA of a net A of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial… (More)

- Paolo Bertozzini, Roberto Conti
- 2008

In the setting of C*-categories, we provide a definition of “spectrum” of a commutative full C*-category as a one-dimensional unital saturated Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gel’fand duality theorem generalizing the usual Gel’fand duality between the categories of commutative unital C*-algebras and… (More)

- Paolo BERTOZZINI, Roberto CONTI
- 2010

This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita–Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care… (More)

- Roberto Conti, Benedetto Allotta, Enrico Meli, Alessandro Ridolfi
- Robotica
- 2017

- Erik Bédos, Roberto Conti
- 2000

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with CCR-representations of bilinear maps. Detailed computations are presented in the case where G is a finitely generated free… (More)

Let F be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if F has trivial superselection structure then every covariant, Haag-dual subsystem B is of the form F 1 ⊗ I for a suitable decomposition F = F1 ⊗ F2 and a compact group action. Then we discuss some application of our… (More)

- Paolo Bertozzini, Roberto Conti
- 2005

In the context of Connes’ spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. Connes’ construction of spectral triples for group algebras is a covariant functor from the category of discrete groups with length functions to that of spectral triples. Several… (More)