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While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [xi, xj ] = iθij. Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [xi, xj ] = ic k ijxk. For all possible threedimensional cases, we define a new… (More)

- Fedele Lizzi, Patrizia Vitale, A . Zampini
- 2003

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)

- Paolo Aschieri, Fedele Lizzi, Patrizia Vitale
- 2007

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)

- Patrizia Vitale
- 1999

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)

- J. M. Gracia-Bondı́a, Fedele Lizzi, Francisco Ruiz, Patrizia Vitale
- 2006

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)

- Olga V. Man’ko, Vladimir I. Man’ko, Giuseppe Marmo, Patrizia Vitale
- 2006

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)

- Lucas Rosa, Patrizia Vitale, Christof Wetterich
- Physical review letters
- 2001

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 present a brief review of the fuzzy disc, the finite algebra approximating functions on a disc, which we have introduced earlier. We also present a comparison with recent papers of Balachandran, Gupta and Kürkçüoǧlu, and of Pinzul and Stern, aimed at the discussion of edge states of a Chern-Simons theory.

- Salvatore Galluccio, Patrizia Vitale, Raffaele Punzi
- 2009

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)