arXiv subjects

Michele Arzano

Publications and source records attributed to Michele Arzano.

At least 37 records · Page 2Linked to original sources

arXiv2020

Conformal quantum mechanics of causal diamonds

It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within the causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the time axis. This indicates that the Unruh temperature perceived by static diamond observers in the vacuum state of inertial observers in Minkowski space can be obtained from the behaviour of the two-point functions of conformal quantum mechanics.

gr-qc↗

arXiv2019

Note on the symplectic structure of asymptotically flat gravity and BMS symmetries

The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving BMS charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add "ad-hoc" boundary terms in the symplectic form. In this note we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the correct Poisson brackets between the boundary fields without any additional assumption. The same Poisson brackets are used to show that BMS charges canonically generate BMS transformations on the gravitational phase space.

gr-qc↗

arXiv2019

A fuzzy bipolar celestial sphere

We introduce a non-commutative deformation of the algebra of bipolar spherical harmonics supporting the action of the full Lorentz algebra. Our construction is close in spirit to the one of the non-commutative spherical harmonics associated to the fuzzy sphere and, as such, it leads to a maximal value of the angular momentum. We derive the action of Lorentz boost generators on such non-commutative spherical harmonics and show that it is compatible with the existence of a maximal angular momentum.

gr-qc↗

arXiv2019

A bound on Planck-scale deformations of CPT from muon lifetime

We show that deformed relativistic kinematics, expected to emerge in a flat-spacetime limit of quantum gravity, predicts different lifetimes for particles and their antiparticles. This phenomenon is a consequence of Planck-scale modifications of the action of discrete symmetries. In particular we focus on deformations of the action of CPT derived from the kappa-Poincare algebra, the most studied example of Planck-scale deformation of relativistic symmetries. Looking at lifetimes of muons and anti-muons we are able to derive an experimental bound on the deformation parameter of kappa > 4x10^14 GeV from measurements at the LHC. Such bound has the potential to reach the value of kappa > 2x10^16 GeV using measurements at the planned Future Circular Collider (FCC).

hep-ph↗

arXiv2019

Quantum ergosphere and brick wall entropy

We revisit the "brick wall" model for black hole entropy taking into account back-reaction effects on the horizon structure. We do so by adopting an evaporating metric in the quasi-static approximation in which departures from the standard Schwarzschild metric are governed by a small luminosity factor. One of the effects of the back-reaction is to create an ergosphere-like region which naturally tames the usual divergence in the calculation of the partition function of the field. The black hole luminosity sets the width of such "quantum ergosphere". We find a finite horizon contribution to the entropy which, for the luminosity associated to the Hawking flux, agrees remarkably well with the Bekenstein-Hawking relation.

gr-qc↗

arXiv2018

Horizon temperature on the real line

We illustrate the analogue of the Unruh effect for a quantum system on the real line. Our derivation relies solely on basic elements of representation theory of the group of affine transformations without a notion of time or metric. Our result shows that a thermal distribution naturally emerges in connecting quantum states belonging to representations associated to distinct notions of translational symmetry.

hep-th↗

arXiv2018

Signal propagation on $κ$-Minkowski spacetime and non-local two-point functions

We study the propagation of quantum fields on $κ$-Minkowsi spacetime. Starting from the non-commutative partition function for a free field written in momentum space we derive the Feynman propagator and analyze the non-trivial singularity structure determined by the group manifold geometry of momentum space. The additional contributions due to such singularity structure result in a deformed field propagation which can be alternatively described in terms of an ordinary field propagation determined by a source with a blurred spacetime profile. We show that the $κ$-deformed Feynman propagator can be written in terms of vacuum expectation values of a commutative non-local quantum field. For sub-Planckian modes the $κ$-deformed propagator corresponds to the vacuum expectation value of the time-ordered product of non-local field operators while for trans-Plankian modes this is replaced by the Hadamard two-point function, the vacuum expectation value of the anti-commutator of non-local field operators.

hep-th↗

arXiv2018

Accelerated horizons and Planck-scale kinematics

We extend the concept of accelerated horizons to the framework of deformed relativistic kinematics at the Planck scale. We show that the non-trivial effects due to symmetry deformation manifest in a finite blueshift for field modes as measured by a Rindler observer approaching the horizon. We investigate whether, at a field theoretic level, this effect could manifest in the possibility of a finite horizon contribution to the entropy, a sort of covariant brick-wall. In the specific model of symmetry deformation considered it will turn out that a non-diverging density of modes close to the horizon can be achieved only by introducing a momentum space measure which violates Lorentz invariance.

gr-qc↗

arXiv2017

Parity at the Planck scale

We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum ${\bf k}$: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by $κ$-Poincaré symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected.

gr-qc↗

arXiv2017

Finite entanglement entropy and spectral dimension in quantum gravity

What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: 1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; 2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.

hep-th↗

arXiv2017

Entanglement entropy, scale-dependent dimensions and the origin of gravity

We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.

hep-th↗

arXiv2017

Relativistic Planck-scale polymer

Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is usually assumed that the discrete polymer structure should lead to a breakdown of relativistic symmetries. We here focus for simplicity on a one-spatial-dimension polymer model and show that relativistic symmetries are deformed, rather than being broken. The specific type of deformed relativistic symmetries which we uncover appears to be closely related to analogous descriptions of relativistic symmetries in some noncommutative spacetimes. This also contributes to an ongoing effort attempting to establish whether the "quantum-Minkowski limit" of Loop Quantum Gravity is a noncommutative spacetime.

gr-qc↗

arXiv2017

Spacetime defects and group momentum space

We study massive and massless conical defects in Minkowski and de Sitter spaces in various spacetime dimensions. The energy-momentum of a defect, considered as an (extended) relativistic object, is completely characterized by the holonomy of the connection associated with its spacetime metric. The possible holonomies are given by Lorentz group elements, which are rotations and null rotations for massive and massless defects respectively. In particular, if we fix the direction of propagation of a massless defect in n+1-dimensional Minkowski space, then its space of holonomies is a maximal abelian subgroup of the AN(n-1) group, which corresponds to the well known momentum space associated with the n-dimensional $κ$-Minkowski noncommutative spacetime and $κ$-deformed Poincaré algebra. We also conjecture that massless defects in n-dimensional de Sitter space can be analogously characterized by holonomies belonging to the same subgroup. This shows how group-valued momenta related to four-dimensional deformations of relativistic symmetries can arise in the description of motion of spacetime defects.

hep-th↗

arXiv2017

Noncommutative fields and the short-scale structure of spacetime

There is a growing evidence that due to quantum gravity effects the effective spacetime dimensionality might change in the UV. In this letter we investigate this hypothesis by using quantum fields to derive the UV behaviour of the static, two point sources potential. We mimic quantum gravity effects by using non-commutative fields associated to a Lie group momentum space with a Planck mass curvature scale. We find that the static potential becomes finite in the short-distance limit. This indicates that quantum gravity effects lead to a dimensional reduction in the UV or, alternatively, that point-like sources are effectively smoothed out by the Planck scale features of the non-commutative quantum fields.

hep-th↗

arXiv2016

UV dimensional reduction to two from group valued momenta

We describe a new model of deformed relativistic kinematics based on the group manifold $U(1) \times SU(2)$ as a four-momentum space. We discuss the action of the Lorentz group on such space and and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by {\it two} energy scales $λ$ and $κ$. A relevant feature of the model is that it exhibits a running spectral dimension $d_s$ with the characteristic short distance reduction to $d_s =2$ found in most quantum gravity scenarios.

hep-th↗

arXiv2016

What gravity waves are telling about quantum spacetime

We discuss various modified dispersion relations motivated by quantum gravity which might affect the propagation of the recently observed gravitational-wave signal of the event GW150914. We find that the bounds set by the data on the characteristic quantum-gravity mass scale $M$ are too weak to constrain these scenarios and, in general, much weaker than the expected $M> 10^4\,\text{eV}$ for a correction to the dispersion relation linear in $1/M$. We illustrate this issue by giving lower bounds on $M$, plus an upper bound coming from constraints on the size of a quantum ergosphere. We also show that a phenomenological dispersion relation $ω^2 = k^2(1+αk^n/M^n)$ is compatible with observations and, at the same time, has a phenomenologically viable mass $M>10\,\text{TeV}$ only in the quite restrictive range $0<n<0.68$. Remarkably, this is the domain of multiscale spacetimes but not of known quantum-gravity models.

gr-qc↗

arXiv2016

Deformed discrete symmetries

We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter kappa to be derived via precision measurements of discrete symmetries and CPT.

hep-th↗

arXiv2016

Deformed phase spaces with group valued momenta

We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the $n$-dimensional generalization of the $κ$-deformed momentum space and the $SL(2, \mathbb{R})$ momentum space in three space-time dimensions. We discuss classical momentum observables associated to multi-particle systems and argue that these combine according the usual four-vector addition despite the non-abelian group structure of momentum space.

hep-th↗