arXiv subjects

Giacomo Rosati

Publications and source records attributed to Giacomo Rosati.

At least 19 recordsLinked to original sources

arXiv2026

κ-deformed spin-1/2 field

In this paper, we investigate the Poincaré and discrete symmetries of a $κ$-deformed spin-$\tfrac12$ field, extending recent results obtained for scalar fields. We construct an action that is Poincaré invariant and analyze its consequences within the deformed framework. Our results confirm the findings of our recent analysis of the $κ$-deformed scalar field, where we established that there is no action invariant under both Poincaré symmetry and charge conjugation in the $κ$-deformed case, while $\mathcal{CPT}$-symmetry can be restored through a natural deformation of time reversal. Furthermore, we present an explicit calculation of the Noether charges associated with Poincaré symmetry and show that their algebra closes, demonstrating the internal consistency of the theory.

hep-th↗

arXiv2026

Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $κ$-field theory

The positive and negative energy modes of a field theory in $κ$-Minkowski/$κ$-Poincaré noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two distinct sectors of a curved momentum space. By performing an explicit direct computation of the relativistic Noether charges and their algebra within the canonical formalism, we identify a striking consequence of this asymmetry in momentum space: charge conjugation and Poincaré invariance are incompatible. We then notice how the structure of momentum space suggests that time reversal could be deformed so that the overall ${\cal C}{\cal P}{\cal T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.

hep-th↗

arXiv2026

DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation

The most active area of research in quantum-gravity phenomenology investigates the possibility of Planck-scale-modified dispersion relations, focusing mainly on two alternative scenarios: the "LIV" scenario, characterized by a specific mechanism of breakdown of relativistic symmetries, and the "DSR" scenario, which preserves overall relativistic invariance but with deformed laws of relativistic transformation. Two recent studies of modified dispersion relations, one relying on Finsler geometry and one based on heuristic reasoning, raised the possibility of potentially observable effects for time dilation and argued that this might apply also to the LIV and DSR scenarios. We observe that the description of Lorentz transformations in the LIV scenario is such that time dilation cannot be modified. The DSR scenario allows for modifications of time dilation, and establishing their magnitude required us to obtain novel results on the effects of finite DSR boosts in the spacetime sector, with results showing in particular that the modification of time dilation is too small for experimental testing.

gr-qc↗

arXiv2025

On testing in-vacuo dispersion with the most energetic neutrinos: KM3-230213A case study

The phenomenology of in-vacuo dispersion, an effect such that quantum properties of spacetime slow down particles proportionally to their energies, has been a very active research area since the advent of the Fermi telescope. One of the assumptions made in this 15-year effort is that the phenomenology of in-vacuo dispersion has a particle-energy sweet spot: the energy of the particle should be large enough to render the analysis immune to source-intrinsic confounding effects but still small enough to facilitate the identification of the source of the particle. We use the gigantic energy of KM3-230213A as an opportunity to challenge this expectation. For a neutrino of a few hundred PeVs a transient source could have been observed at lower energies several years earlier, even assuming the characteristic scale of in-vacuo dispersion to be close to the Planck scale. We report that GRB090401B is in excellent directional agreement with KM3-230213A, and we discuss a strategy of in-vacuo-dispersion analysis suitable for estimating the significance of KM3-230213A as a GRB090401B-neutrino candidate. The $p$-value resulting from our analysis (0.015) is not small enough to warrant any excitement, but small enough to establish the point that a handful of such coincidences would be sufficient to meaningfully test in-vacuo dispersion.

astro-ph.HE↗

arXiv2025

Redshift leverage for the search of GRB neutrinos affected by quantum properties of spacetime

Some previous studies based on IceCube neutrinos had found intriguing preliminary evidence that some of them might be GRB neutrinos with travel times affected by quantum properties of spacetime delaying them proportionally to their energy, an effect often labeled as "quantum-spacetime-induced in-vacuo dispersion". Those previous studies looked for candidate GRB neutrinos in a fixed (neutrino-energy-independent) time window after the GRB onset and relied rather crucially on crude estimates of the redshift of GRBs whose redshift has not been measured. We here introduce a complementary approach to the search of quantum-spacetime-affected GRB neutrinos which restricts the analysis to GRBs of sharply known redshift, and, in a way that we argue is synergistic with having sharp information on redshift, adopts a neutrino-energy-dependent time window. We find that knowing the redshift of the GRBs strengthens the analysis enough to compensate for the fact that of course the restriction to GRBs of known redshift reduces the number of candidate GRB neutrinos. And rather remarkably our estimate of the magnitude of the in-vacuo-dispersion effects is fully consistent with what had been found using the previous approach. Our findings are still inconclusive, since their significance is quantified by a $p$-value of little less than $0.01$, but provide motivation for monitoring the accrual of neutrino observations by IceCube and KM3NeT as well as for further refinements of the strategy of analysis here proposed.

gr-qc↗

arXiv2023

Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime

Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR) for the constant-curvature case. We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also derive a generalization of our results to the FRW case, and discuss some specific combinations of the three forms of redshift dependence whose investigation might deserve priority from the quantum-gravity perspective.

gr-qc↗

arXiv2022

Could quantum gravity slow down neutrinos?

In addition to its implications for astrophysics, the hunt for GRB neutrinos could also be significant in quantum-gravity research, since they are excellent probes of the microscopic fabric of spacetime. Some previous studies based on IceCube neutrinos had found intriguing preliminary evidence that some of them might be GRB neutrinos with travel times affected by quantum properties of spacetime, with the noticeable feature that quantum spacetime would slow down some of the neutrinos while others would be sped up. Recently the IceCube collaboration revised significantly the estimates of the direction of observation of their neutrinos, and we here investigate how the corrected directional information affects the results of the previous quantum-spacetime-inspired analyses. We find that there is now no evidence for neutrinos sped up by quantum-spacetime properties, whereas the evidence for neutrinos slowed down by quantum spacetime is even stronger than previously found. Our most conservative estimates find a false alarm probability of less than 1% for these "slow neutrinos", providing motivation for future studies on larger data samples.

gr-qc↗

arXiv2021

Covariant four dimensional differential calculus in $κ$-Minkowski

It is generally believed that it is not possible to have a four dimensional differential calculus in $κ$-Minkowski spacetime, with $κ$-Poincaré relativistic symmetries, covariant under ($κ$-deformed) Lorentz transformations. Thus, one usually introduces a fifth differential form, whose physical interpretation is still challenging, and defines a covariant five dimensional calculus. Nevertheless, the four dimensional calculus is at the basis of several works based on $κ$-Minkowski/$κ$-Poincaré framework that led to meaningful insights on its physical interpretation and phenomenological implications. We here revisit the argument against the covariance of the four dimensional calculus, and find that it depends crucially on an incomplete characterization of Lorentz transformations in this framework. In particular, we understand that this is due to a feature, still uncovered at the time, that turns out to be fundamental for the consistency of the relativistic framework: the noncommutativity of the Lorentz transformation parameters. Once this is taken into account, the four dimensional calculus is found to be fully Lorentz covariant. The result we obtain extends naturally to the whole $κ$-Poincaré algebra of transformations, showing the close relation between its relativistic nature and the properties of the differential calculus.

hep-th↗

arXiv2021

$κ$-deformed complex fields and discrete symmetries

We present a construction of $κ$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that, in order to have an appropriate action of Lorentz symmetries on antiparticle states, these should be described by four-momenta living on the complement of the portion of de Sitter group manifold to which $κ$-deformed particle four-momenta belong. Once the equations of motions are properly worked out from the deformed action we obtain that particle and antiparticle are characterized by different mass-shell constraints leading to a subtle form of departure from CPT invariance. The remaining part of our work is dedicated to a detailed description of the action of deformed Poincaré and discrete symmetries on the complex field.

hep-th↗

arXiv2020

Phenomenology of curvature-induced quantum-gravity effects

Several studies have been devoted to the possibility that quantum gravity might tangibly affect relativistic kinematics for particles propagating from distant astrophysical sources to our telescopes, but the relevant literature has so far focused exclusively on a subclass of scenarios such that the quantum-gravity effects are independent of (macroscopic) curvature. It was assumed that a phenomenology for quantum-gravity effects that are triggered by curvature might be a dead end because of a double suppression: by the smallness of the characteristic quantum-gravity length scale and by the smallness of curvature. This state of affairs is becoming increasingly unsatisfactory in light of some recent quantum-gravity studies providing evidence of the fact that the presence of curvature might be required in order to have the novel relativistic properties. We here analyze an explicit scenario for curvature-induced quantum-gravity effects, and show that the smallness of curvature does not pose a challenge for phenomenology since it is compensated by the large distances traveled by the particles considered in the relevant phenomenological studies. We also observe that the present data situation for particles propagating from distant astrophysical sources to our telescopes, while inconclusive, provides more encouragement for our curvature-induced effects than for the curvature-independent effects that were so far studied.

gr-qc↗

arXiv2020

Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space

We study the implications of a change of coordinatization of momentum space for theories with curved momentum space. We of course find that after a passive diffeomorphism the theory yields the same physical predictions, as one would expect considering that a simple reparametrization should not change physics. However, it appears that general momentum-space covariance (invariance under active diffeomorphisms of momentum space) cannot be enforced, and within a given set of prescriptions on how the theory should encode momentum-space metric and affine connection the physical predictions do depend on the momentum space background. These conclusions find support in some general arguments and in our quantitative analysis of a much-studied toy model with maximally-symmetric (curved) momentum space.

gr-qc↗

arXiv2019

Path integral quantization of a spinning particle

Following the idea of Alekseev and Shatashvili we derive the path integral quantization of a modified relativistic particle action that results in the Feynman propagator of a free field with arbitrary spin. This propagator can be associated with the Duffin, Kemmer, and Petiau (DKP) form of a free field theory. We show explicitly that the obtained DKP propagator is equivalent to the standard one, for spins 0 and 1. We argue that this equivalence holds also for higher spins.

hep-th↗

arXiv2019

Physical velocity of particles in relativistic curved momentum space

We show in general that for a relativistic theory with curved momentum space, i.e.~a theory with deformed relativistic symmetries, the physical velocity of particles coincides with their group velocity. This clarifies a long-standing question about the discrepancy between coordinate and group velocity for this kind of theories. The first evidence that this was the case had been obtained at linear order in the deformation parameter in Phys.Lett.B700(2011)150 for the specific case of $κ$-momentum space. The proof was based on the recent understanding of how relative locality affects these scenarios. We here rely again on a careful implementation of relative locality effects, and obtain our result for a generic (relativistic) curved momentum space framework at all orders in the deformation/curvature parameter. We also discuss the validity of this result when the deformation depends on the coordinates as well as on the momenta.

gr-qc↗

arXiv2018

Non-commutative Fourier transform for the Lorentz group via the Duflo map

We defined a non-commutative algebra representation for quantum systems whose phase space is the cotangent bundle of the Lorentz group, and the non-commutative Fourier transform ensuring the unitary equivalence with the standard group representation. Our construction is from first principles in the sense that all structures are derived from the choice of quantization map for the classical system, the Duflo quantization map.

hep-th↗

arXiv2018

Relative-locality phenomenology on Snyder spacetime

We study the effects of relative locality dynamics in the case of the Snyder model. Several properties of this model differ from those of the widely studied $κ$-Poincaré models: for example, in the Snyder case the action of the Lorentz group is preserved, and the composition law of momenta is deformed by terms quadratic in the inverse Planck energy. From the investigation of time delay and dual curvature lensing we deduce that, because of these differences, in the Snyder case the properties of the detector are essential for the observation of relative locality effects. The deviations from special relativity do not depend on the energy of the particles and are much smaller than in the $κ$-Poincaré case, so that are beyond the reach of present astrophysical experiments. However, these results have a conceptual interest, because they show that relative-locality effects can occur even if the action of the Lorentz group on phase space is not deformed.

gr-qc↗

arXiv2017

$κ$-de Sitter and $κ$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant

Defining a new r-matrix compatible with the scalar product at the basis of the Chern-Simons action for a particle coupled to (2+1) Lorentzian gravity with cosmological constant, I show how deformed symmetries of $κ$-de Sitter and, in the vanishing cosmological limit, of $κ$-Poincaré kind, arise naturally as quantum-deformation of three dimensional gravity. I obtain moreover the non-commutative spacetime associated to these kinds of symmetries.

hep-th↗

arXiv2016

In-vacuo-dispersion features for GRB neutrinos and photons

Over the last 15 years there has been considerable interest in the possibility of quantum-gravity-induced in-vacuo dispersion, the possibility that spacetime itself might behave essentially like a dispersive medium for particle propagation. Two very recent studies have exposed what might be in-vacuo dispersion features for GRB (gamma-ray-burst) neutrinos of energy in the range of 100 TeV and for GRB photons with energy in the range of 10 GeV. We here show that these two features are roughly compatible with a description such that the same effects apply over 4 orders of magnitude in energy. We also characterize quantitatively how rare it would be for such features to arise accidentally, as a result of (still unknown) aspects of the mechanisms producing photons at GRBs or as a result of background neutrinos accidentally fitting the profile of a GRB neutrino affected by in-vacuo dispersion.

astro-ph.HE↗

arXiv2016

Symmetries of quantum space-time in 3 dimensions

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $Λ$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of $so_q(4)$, with $ q = \exp{(i\hbar \sqrtΛ/2κ)}$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $κ$ finite, we obtain the kappa-Poincaré algebra of the flat quantum space-time symmetries.

hep-th↗