arXiv subjects

S. Mignemi

Publications and source records attributed to S. Mignemi.

At least 19 recordsLinked to original sources

arXiv2026

Dyonic black holes from dimensional reduction of five-dimensional Einstein-Gauss-Bonnet gravity

We study the general black hole solutions of dimensionally reduced five-dimensional Einstein-Gauss-Bonnet gravity. The reduced theory contains gravity, electromagnetism and a scalar field, with nonlinear corrections to the action and nontrivial couplings. The solutions can be classified through mass and electric and magnetic charge. They present peculiar features with respect to the solutions of the standard Kaluza-Klein theory without Gauss-Bonnet corrections, like the existence of an extremal mass even in the neutral case. Also the thermodynamics is affected, for example, extremal black holes display nonvanishing temperature and entropy.

gr-qc↗

arXiv2025

CPT breaking in noncommutative Magueijo-Smolin model

We review an instance of noncommutative geometry based on a specific realization of the model of doubly special relativity proposed by Magueijo and Smolin (MS) on noncommutative spacetime. In particular, we discuss the Hopf algebra associated to it, which has not been considered in the literature till now. We show that the momentum sector of this model can be viewed as a particular basis of the \kp model. An interesting property is that the MS Hamiltonian is not invariant under the reversal of the sign of the energy, and in particular it is not invariant under the standard definition of charge conjugation. Therefore, if following Dirac one identifies the negative energy states with antiparticles, their mass differs from that of particles. We examine the possible consequences of this fact in the context of first quantization and discuss its interpretation from the point of view of quantum field theory, taking into account possible alternative definitions of charge conjugation proposed in the noncommutative framework.

hep-th↗

arXiv2025

Dual $\kappa$-Minkowski spaces and $\kappa$-Poincar\'{e} algebras from Yang model and their Weyl realizations

We consider the Yang algebras isomorphic to $o(1,5), o(2,4), o(3,3)$ and derive dual $\kappa$-Minkowski and $\kappa$-Poincar\'{e} algebras in terms of a metric $g$. The corresponding Weyl realization is presented and coproduct, star product and twist are computed in terms of the metric $g$. Finally, we construct reduced $\kappa$-Minkowski and $\kappa$-Poincar\'{e} algebras as special cases.

hep-th↗

arXiv2025

Reduced Yang model and noncommutative geometry of curved spacetime

The Yang model describes a noncommutative geometry in a curved spacetime by means of an orthogonal algebra $o(1,5)$, whose 15 generators are identified with phase space variables and Lorentz generators together with an additional scalar generator. In this paper we show that it is possible to define a nonlinear algebra with the same structure, but with only 14 generators, that better fits in phase space. The fifteenth generator of the Yang algebra can then be written as a function of the squares of the others. As a simple application, we also consider the problem of the quantum harmonic oscillator in this theory, calculating the energy spectrum in the one- and three-dimensional nonrelativistic versions of the model.

hep-th↗

arXiv2025

Yang model revisited

A long time ago C.N. Yang proposed a generalization of the Snyder model to the case of a curved background spacetime, based on an algebra isomorphic to $so(1,5)$, which includes as subalgebras both the Snyder and the de Sitter algebras. His proposal can therefore be interpreted as a model of noncommutative curved spacetime, and could be useful for relating physics at very small and very large scales. We review this model and some recent progress concerning its generalizations and its interpretation in the framework of Hopf algebras. We also report some possibilities to relate it to more phenomenological aspects.

hep-th↗

arXiv2024

Quantum mechanics of the nonrelativistic Yang model

We discuss, at leading order in $\hbar$, the quantum mechanics of a specific realization in phase space of the Yang model describing noncommutative geometry in a curved background. In particular, we show how the deformation of the Heisenberg uncertainty relations crucially depends on the signs of the coupling constants of the model. We also discuss the dynamics of the free particle and of the harmonic oscillator. Also in this case the results depend on the signs of the coupling constants.

hep-th↗

arXiv2024

If the universe were curved and noncommutative

We review recent discussions concerning the definition of a quantum field theory in a curved and noncommutative space, the Snyder--de Sitter space. For a quartic self-interacting scalar field in a spacetime of arbitrary dimension, we show how to perturbatively define the classical action in the small-deformation regime and give its explicit first-order expression. Afterwards, we compute the divergences of the one-loop effective action for the two- and four-dimensional cases. These are employed to calculate the beta functions of the couplings and to numerically analyze the corresponding renormalization group flow. Depending on the initial conditions of the couplings, in four dimensions it is possible to obtain an asymptotic-free theory or a flip in the sign of the cosmological constant as a consequence of the running.

hep-th↗

arXiv2024

Realizations and star-product of doubly $\kappa$-deformed Yang models

The Yang algebra was proposed a long time ago as a generalization of the Snyder algebra to the case of curved background spacetime. It includes as subalgebras both the Snyder and the de Sitter algebras and can therefore be viewed as a model of noncommutative curved spacetime. A peculiarity with respect to standard models of noncommutative geometry is that it includes translation and Lorentz generators, so that the definition of a Hopf algebra and the physical interpretation of the variables conjugated to the primary ones is not trivial. In this paper we consider the realizations of the Yang algebra and its $\kappa$-deformed generalization on an extended phase space and in this way we are able to define a Hopf structure and a twist.

hep-th↗

arXiv2023

Dyonic black holes in Kaluza-Klein theory with a Gauss-Bonnet action

We consider a five-dimensional Einstein-Gauss-Bonnet model, which gives rise after dimensional reduction to Einstein gravity nonminimally coupled to nonlinear electrodynamics. The black hole solutions of the four-dimensional model modify the Reissner-Nordstrom solutions of general relativity. The gravitational field presents the standard singularity at $r=0$, while the electric field can be regular everywhere if the magnetic charge vanishes

gr-qc↗

arXiv2023

Realizations of the Yang-Poisson model on canonical phase space

We discuss exact realizations of the Yang-Poisson model on canonical phase space. The Yang model is an example of noncommutative geometry on a background spacetime of constant curvature and is notable for its duality between position and momentum manifolds. We call Yang-Poisson model its classical limit, with commutators replaced by Poisson brackets. The structure is simpler in the classical case, and exact realizations can be found.

hep-th↗

arXiv2023

Hermitian realizations of the Yang model

The Yang model is an example of noncommutative geometry on a background spacetime of constant curvature. We discuss the Hermitian realizations of its associated algebra on phase space in a perturbative expansion up to sixth order. We also discuss its realizations on extended phase spaces, that include additional tensorial and/or vectorial degrees or freedom.

hep-th↗

arXiv2023

The beauty of curved momentum space

In this manuscript, we will discuss the notion of curved momentum space, as it arises in the discussion of noncommutative or doubly special relativity theories. We will illustrate it with two simple examples, the Casimir effect in anti-Snyder space and the introduction of fermions in doubly special relativity. We will point out the existence of intriguing results, which suggest nontrivial connections with spectral geometry and Hopf algebras.

hep-th↗

arXiv2022

Noncommutative Yang model and its generalizations

Long time ago, C.N. Yang proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper we review his proposal and the generalizations that have been suggested during the years. In particular, we discuss the most general algebras that contain as subalgebras both de Sitter and Snyder algebras, preserving Lorentz invariance, and are generated by a two-parameter deformation of the canonical Heisenberg algebra. We also define their realizations on quantum phase space, giving explicit examples, both exact and in terms of a perturbative expansion in the deformation parameters.

gr-qc↗

arXiv2022

Quantum mechanics of the extended Snyder model

We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial degrees of freedom, together with their conjugate momenta. The \coo obey nontrivial \cor and generate a noncommutative geometry, which admits nicer properties than the usual realization of the model, in particular giving rise to an associative star product. The spectrum of the harmonic oscillator is studied through the introduction of creation and annihilation operators. Some physical consequences of the introduction of the additional degrees of freedom are discussed.

quant-ph↗

arXiv2022

Generalizations of Snyder model to curved spaces

We consider generalizations of the Snyder algebra to a curved spacetime background with de Sitter symmetry. As special cases, we obtain the algebras of the Yang model and of triply special relativity. We discuss the realizations of these algebras in terms of canonical phase space coordinates, up to fourth order in the deformation parameters. In the case of triply special relativity we also find exact realization, exploiting its algebraic relation with the Snyder model.

hep-th↗

arXiv2021

Dyonic black holes in nonlinear electrodynamic from Kaluza-Klein theory with a Gauss-Bonnet term

Five-dimensional Kaluza-Klein theory with an Einstein-Gauss-Bonnet Lagrangian induces nonlinear corrections to the four-dimensional Maxwell equations, which however remain second order. Although these corrections do not have effect on the purely electric or magnetic monopole solutions for pointlike charges, they affect the dyonic solutions, smoothing the electric field at the origin for negative values of the Gauss-Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of gravity, obtaining charged black hole solutions that generalize the Reissner-Nordstr\"om metric.

gr-qc↗

arXiv2021

Associative realizations of $\kappa$-deformed extended Snyder model

Usually, the realizations of the noncommutative Snyder model lead to a nonassociative star product. However, it has been shown that this problem can be avoided by adding to the spacetime coordinates new tensorial degrees of freedom. The model so obtained, called extended Snyder model, can be subject to a $\kappa$-deformation, giving rise to a unification of the Snyder and the $\kappa$-Poincar\'e algebras in the formalism of extended spacetime. In this paper we review this construction and consider the generic realizations of the $\kappa$-deformed extended Snyder model, calculating the associated star product, coproduct and twist in a perturbative setting. We also introduce a representation of the Lorentz algebra in the extended space and speculate on possible interpretations of the tensorial degrees of freedom.

physics.gen-ph↗

arXiv2021

The Snyder-de Sitter Scalar $\varphi^4_{\star}$ Quantum Field Theory in D=2

We study the two-dimensional version of a quartic self-interacting quantum scalar field on a curved and noncommutative space (Snyder-de Sitter). We show that the model is renormalizable at the one-loop level and compute the beta functions of the related couplings. The renormalization group flow is then studied numerically, arriving at the conclusion that noncommutative-curved deformations can yield both relevant and irrelevant contributions to the one-loop effective action.

hep-th↗