arXiv subjects

S. Mignemi

Publications and source records attributed to S. Mignemi.

At least 37 records · Page 2Linked to original sources

arXiv2021

The Snyder-de Sitter Scalar $φ^4_{\star}$ 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↗

arXiv2021

Worldline Formalism in Snyder Spaces

We study the $ϕ_{\star}^4$ model for a scalar field in a linearization of the Snyder model, using the methods of the Worldline Formalism. Our main result is a master equation for the 1-loop n-point function. From this we derive the renormalization of the coupling parameters of the theory and observe the appearance of a $ϕ^6$ divergent contribution that opens the question of whether this theory is renormalizable or not. Additionally, we observe that some terms in the renormalized action can be interpreted as coming from an effective metric proportional to the square of the field.

hep-th↗

arXiv2021

Unification of $κ$-Minkowski and extended Snyder spaces

In a recent paper, we have studied associative realizations of the noncommutative extended Snyder model, obtained by including the Lorentz generators (tensorial coordinates) and their conjugated momenta. In this paper, we extend this result to also incorporate a covariant realization of the $κ$-Poincaré spacetime. We obtain the coproduct, the associative star product and the twist in a Weyl-ordered realization, to first order in the noncommutativity parameters. This could help the construction of a quantum field theory based on this geometry.

hep-th↗

arXiv2020

Associative realizations of the extended Snyder model

The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.

physics.gen-ph↗

arXiv2020

Casimir effect in Snyder Space

We show that two indistinguishable aspects of the divergences occurring in the Casimir effect, namely the divergence of the energy of the higher modes and the non-com\-pact\-ness of the momentum space, get disentangled in a given noncommutative setup. To this end, we consider a scalar field between two parallel plates in an anti-Snyder space. Additionally, the large mass decay in this noncommutative setup is not necessarily exponential.

hep-th↗

arXiv2019

The Snyder model and quantum field theory

We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutaive QFT and discuss the possibility of obtaining a finite theory.

hep-th↗

arXiv2019

Cyclotron frequency and the quantum clock

We discuss the corrections to the orbital period of a particle in a constant magnetic field, driven by the model of noncommutative geometry recently associated to a quantum clock. The effects are extremely small, but in principle detectable.

physics.gen-ph↗

arXiv2019

$κ$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

We consider $κ$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincaré algebra is unaltered, while the other is a general extension where the Poincaré algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincaré-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincaré-Weyl algebra.

hep-th↗

arXiv2019

Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.

hep-th↗

arXiv2017

Vacuum energy from noncommutative models

The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.

hep-th↗

arXiv2017

Relative-locality geometry for the Snyder model

We investigate the geometry of the energy-momentum space of the Snyder model of noncommmutative geometry and of its generalizations, according to the postulates of relative locality. These relate the geometric structures to the deformed composition law of momenta. It turns out that the Snyder energy-momentum spaces are maximally symmetric, with vanishing torsion and nonmetricity. However, one cannot apply straightforwardly the phenomenological relations between the geometry and the dynamics postulated in the standard prescription of relative locality, because they were obtained assuming that the leading corrections to the composition law of momenta are quadratic, which is not the case with the Snyder model and its generalizations

hep-th↗

arXiv2017

Snyder-type spaces, twisted Poincaré algebra and addition of momenta

We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry. The corresponding deformed addition of momenta, the twist and the $R$-matrix are calculated to first order in the deformation parameters for all models. In the particular case of the Snyder realisation, the exact formula for the twist is obtained.

hep-th↗

arXiv2017

Quantum field theory in generalised Snyder spaces

We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate peturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

hep-th↗

arXiv2016

Relative-locality effects in Snyder spacetime

When applied to some models of noncommutative geometry, the formalism of relative locality predicts the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. This conclusion is in accordance with the findings of doubly special relativity. Distant observers may however measure different times of flight for massive particle.

hep-th↗

arXiv2016

Generalized relativistic kinematics in Poincaré-invariant models

Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincaré invariance that preserves the Poincaré algebra, and only modifies its action on phase space in a Lorentz-invariant way. We show that, in contrast to the case where the Poincaré algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We give some nontrivial examples of this arising from doubly special relativity and noncommutative geometry and show that Hopf-algebra methods give equivalent results.

hep-th↗

arXiv2016

Quantum mechanics on a curved Snyder space

We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the Born reciprocity for exchange of positions and momenta. Its representations can be obtained starting from those of the Snyder algebra, and exploiting the geometrical properties of the phase space, that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum.

hep-th↗

arXiv2015

Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation

We study the spectrum of the hydrogen atom in Snyder space in a semiclassical approximation based on a generalization of the Born-Sommerfeld quantization rule. While the corrections to the standard quantum mechanical spectrum arise at first order in the Snyder parameter for the $l=0$ states, they are of second order for $l\neq 0$. This can be understood as due to the different topology of the regions of integration in phase space.

quant-ph↗

arXiv2015

Path integrals in Snyder space

The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw.

hep-th↗