Patrizia Vitale

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We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characterizing the noncommutative plane with a ∗ product and depends on two parameters N and θ. It is composed of functions which decay exponentially outside a disc. In the limit in which(More)
We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields,(More)
The large N limit of the Gross–Neveu model is here studied on manifolds with constant curvature, at zero and finite temperature. Using the ζ–function regularization, the phase structure is investigated for arbitrary values of the coupling constant. The critical surface where the second order phase transition takes place is analytically found for both the(More)
We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an x; -space where the spacetime coordinates and the noncommutativity matrix components are on the same footing, we obtain a noncommutative representation of the affine algebra, its generators being differential operators in x;(More)
The transition from quantum to classical mechanics has been an important research subject since the beginning of quantum mechanics (see [1, 2] for a review). A suitable setting for this problem is represented by the Wigner-Weyl-Moyal formalism where the operators corresponding to observables and the states, considered as linear functionals on the space of(More)
The phase transition of the Gross-Neveu model with N fermions is investigated by means of a nonperturbative evolution equation for the scale dependence of the effective average action. The critical exponents and scaling amplitudes are calculated for various values of N in d = 3. It is also explicitly verified that the Neveu-Yukawa model belongs to the same(More)
We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Grönewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given(More)