Massless scalar free Field in 1+1 dimensions I: Weyl algebras Products and Superselection Sectors

This is the first of two papers on the superselection sectors of the conformal model in the title, in a time zero formulation. A classification of the sectors of the net of observables as restrictions of solitonic (twisted) and non-solitonic (untwisted) sector automorphisms of proper extensions of the observable net is given. All of them are implemented by the elements of a field net in a non-regular vacuum representation and the existence of a global compact Abelian gauge group is proved. A non-trivial center in the fixed-point net of this gauge group appears, but in an unphysical representation and reducing to the identity in the physical one. The completeness of the described superselection structure, to which the second paper is devoted, is shown in terms of Roberts' net cohomology. Some general features of physical field models defined by twisted cross products of Weyl algebras in non-regular representations are also presented.Comment: published final versio

The constitutional consequences of financial crisis and the use of emergency powers. flexibility and emergency sources

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the new challenge of constitutional courts is take into considerations both rights and powers , national protctions and immigrations flows. the deep problem is to extend the national guarantee to the non citoyens people

Causal posets, loops and the construction of nets of local algebras for QFT

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 inclusion order relation, we define groups of closed paths (loops) formed by the elements of K. These groups come equipped with a causal disjointness relation and an action of the symmetry group of the spacetime. In this way the local algebras of the net are the group C*-algebras of the groups of loops, quotiented by the causal disjointness relation. We also provide a geometric interpretation of a class of representations of this net in terms of causal and covariant connections of the poset K. In the case of the Minkowski spacetime, we prove the existence of Poincar\'e covariant representations satisfying the spectrum condition. This is obtained by virtue of a remarkable feature of our construction: any Hermitian scalar quantum field defines causal and covariant connections of K. Similar results hold for the chiral spacetime $S^1$ with conformal symmetry

Il Senato della riforma tra forma e sostanza

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The universal C*-algebra of the electromagnetic field

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 are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.Comment: 17 pages, 1 figure; v2: minor corrections, version as to appear in Lett. Math. Phys. Dedicated to the memory of D. Kastler and J.E. Roberts; v3 improvement of layou

La riforma del titolo v e il contenzioso di fronte alla corte costituzionale

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