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Patrizia Vitale

Publications and source records attributed to Patrizia Vitale.

70 records · Page 4Linked to original sources
arXiv2010

Curing the UV/IR mixing for field theories with translation-invariant $\star$ products

The ultraviolet/infrared (UV/IR) mixing of noncommutative field theories has been recently shown to be a generic feature of translation- invariant associative products. In this paper we propose to take into account the quantum corrections of the model to modify in this way the noncommutative action. This idea was already used to cure the UV/IR mixing for theories on Moyal space. We show that in the present framework also, this proposal proves successful for curing the mixing. We achieve this task by explicit calculations of one and higher loops Feynman amplitudes. For the sake of completeness, we compute the form of the new action in the matrix base for the Wick-Voros product.

hep-th↗
arXiv2009

Monopole-based quantization: a programme

We describe a programme to quantize a particle in the field of a (three dimensional) magnetic monopole using a Weyl system. We propose using the mapping of position and momenta as operators on a quaternionic Hilbert module following the work of Emch and Jadczyk.

math-ph↗
arXiv2009

Star-product in the presence of a monopole

We present a deformed star-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in hbar) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.

math-ph↗
arXiv2009

Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-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 by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this with an explicit calculation for represented generic products.

hep-th↗
arXiv2008

Twisted Noncommutative Field Theory: Wick-Voros vs Moyal

We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green's functions and S-matrix. We find that while the Green's functions are different for the two theories, the S-matrix is the same in both cases, and is different from the commutative case.

hep-th↗
arXiv2008

Noncommutative field theory with the Wick-Voros product

We study the noncommutative scalar field theory in the presence of the Wick-Voros product (or normally ordered product), a variant of the more studied Moyal product. We discuss both the classical and the quantum field theory in the quartic potential case, and calculate the Green's functions up to one loop, for the two and four points cases.

hep-th↗
arXiv2008

Noncommutative Conformal Field Theory in the Twist-deformed context

We discuss conformal symmetry on the two dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry.

hep-th↗
arXiv2007

Twisting all the way: from Classical Mechanics to Quantum Fields

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, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative spacetime, i.e. we establish a noncommutative correspondence principle from *-Poisson brackets to *-commutators. In particular commutation relations among creation and annihilation operators are deduced.

hep-th↗
arXiv2006

Star products, duality and double Lie algebras

Quantization of classical systems using the star-product of symbols of observables is discussed. In the star-product scheme an analysis of dual structures is performed and a physical interpretation is proposed. At the Lie algebra level duality is shown to be connected to double Lie algebras. The analysis is specified to quantum tomography. The classical tomographic Poisson bracket is found.

quant-ph↗
arXiv2006

Noncommutative spacetime symmetries: Twist versus covariance

We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,Θ)$-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 $(x,Θ)$-space. As a particular case, the Weyl Lie algebra is studied and known results for Weyl invariant noncommutative field theories are rederived in a nutshell. We also show that this covariance cannot be extended to spacetime transformations generated by differential operators whose coefficients are polynomials of order larger than one. We compare our approach with the twist-deformed enveloping algebra description of spacetime transformations.

hep-th↗
arXiv2005

On the Absence of Continuous Symmetries for Noncommutative 3-Spheres

A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whether or not this property can be extended to the noncommutative three-spheres of Connes and Dubois-Violette. Upon restricting to quantum groups which are continuous deformations of Spin(4) and SO(4) with standard co-actions, our results suggest that this is not the case.

hep-th↗
arXiv2005

The beat of a fuzzy drum: fuzzy Bessel functions for the disc

The fuzzy disc is a matrix approximation of the functions on a disc which preserves rotational symmetry. In this paper we introduce a basis for the algebra of functions on the fuzzy disc in terms of the eigenfunctions of a properly defined fuzzy Laplacian. In the commutative limit they tend to the eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of the first kind, thus deserving the name of fuzzy Bessel functions.

hep-th↗
arXiv2002

On the SO(2,1) symmetry in General Relativity

The role of the SO(2,1) symmetry in General Relativity is analyzed. Cosmological solutions of Einstein field equations invariant with respect to a space-like Lie algebra G_r, with r between 3 and 6 and containing so(2,1) as a subalgebra, are also classified.

gr-qc↗
arXiv1999

Temperature induced phase transitions in four fermion models in curved space-time

The large N limit of the Gross-Neveu model is here studied on manifolds with constant curvature, at zero and finite temperature. Using the zeta-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 positive and negative curvature cases. For negative curvature, where the symmetry is always broken at zero temperature, the mass gap is calculated. The free energy density is evaluated at criticality and the zero curvature and zero temperature limits are discussed.

hep-th↗
arXiv1996

Three Dimensional Gross-Neveu Model on Curved Spaces

The large N limit of the 3-d Gross-Neveu model is here studied on manifolds with positive and negative constant curvature. Using the $ζ$-function regularization we analyze the critical properties of this model on the spaces $S^2 \times S^1$ and $H^2\times S^1$. We evaluate the free energy density, the spontaneous magnetization and the correlation length at the ultraviolet fixed point. The limit $S^1\to R$, which is interpreted as the zero temperature limit, is also studied.

hep-th↗