Roberto Conti

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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)
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)
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)
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)
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)