arXiv subjects

Michele Arzano

Publications and source records attributed to Michele Arzano.

At least 73 records · Page 4Linked to original sources

arXiv2011

Anomalous dimension in semiclassical gravity

The description of the phase space of relativistic particles coupled to three-dimensional Einstein gravity requires momenta which are coordinates on a group manifold rather than on ordinary Minkowski space. The corresponding field theory turns out to be a non-commutative field theory on configuration space and a group field theory on momentum space. Using basic non-commutative Fourier transform tools we introduce the notion of non-commutative heat-kernel associated with the Laplacian on the non-commutative configuration space. We show that the spectral dimension associated to the non-commutative heat kernel varies with the scale reaching a non-integer value smaller than three for Planckian diffusion scales.

gr-qc↗

arXiv2011

Relative-locality distant observers and the phenomenology of momentum-space geometry

We study the translational invariance of the relative-locality framework proposed in arXiv:1101.0931, which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a $κ$-Poincaré-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory simultaneously-emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of arXiv:1103.5626 on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of arXiv:1102.4637 are reproduced. We establish that the torsion of the $κ$-Poincaré connection introduces a small (but observably-large) dependence of the time of detection, for simultaneously-emitted particles, on some properties of the interactions producing the particles at the source.

hep-th↗

arXiv2011

Anatomy of a deformed symmetry: field quantization on curved momentum space

In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of kappa-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for kappa-quantum fields.

hep-th↗

arXiv2010

Kinematics of a relativistic particle with de Sitter momentum space

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.

hep-th↗

arXiv2009

Fun from none: deformed symmetries and Fock space

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $κ$-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibnitz rule. We explore the richer structure of the $κ$-Fock space and point out possible physical consequences of the deformation.

hep-th↗

arXiv2008

Rainbow statistics

Non-commutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a non-trivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of $κ$-quantum fields and discuss the analogies/differences with models with twisted statistics.

hep-th↗

arXiv2008

Hidden entanglement at the Planck scale: loss of unitarity and the information paradox

We discuss how relaxing the requirement of locality for quantum fields can equip the Hilbert space of the theory with a richer structure in its multi-particle sector. A physical consequence is the emergence of a "planckian" mode-entanglement, invisible to an observer that cannot probe the Planck scale. To the same observer, certain unitary processes would appear non-unitary. We show how entanglement transfer to the additional degrees of freedom can provide a potential way out of the black hole information paradox.

hep-th↗

arXiv2008

Quantum fields, non-locality and quantum group symmetries

We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be described within the usual framework of Lie algebras but rather in terms of non-co-commutative Hopf algebras or "quantum groups". Similar "quantizations" of space-time symmetries are expected to emerge in the low-energy limit of certain quantum gravity models and have been used to describe the symmetries of various non-commutative space-times. Our result provides an intuitive characterization of the mechanism that could lead to the emergence of deformed co-products in models of quantum relativistic symmetries.

hep-th↗

arXiv2007

Quantum fields, Noether charges and κ-spacetime symmetries

We discuss how the symmetries of $κ$-Minkowski non-commutative spacetime can be described by the $κ$-Poincaré Hopf algebra. In particular, we focus on a generalization of the Noether analysis in the $κ$-deformed framework which allows us to introduce Noether charges associated with translational symmetries and makes possible to overcome the apparent ambiguities that seemed to be associated with the action of such symmetries. Moving from the classical to the quantum framework, we will first review past results on path integral quantization of a scalar self-interacting field. We will then show how recent work on the symplectic structure of classical $κ$-fields suggests a new approach to the canonical quantization of free fields and and present some new results.

hep-th↗

arXiv2007

Fock space, quantum fields and kappa-Poincaré symmetries

We study the quantization of a linear scalar field, whose symmetries are described by the kappa-Poincare' Hopf-algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (planckian) cut-off for the field modes. At the multi-particle level the non-trivial co-algebra structure of kappa-Poincare' leads to a deformed bosonization in the construction of Fock space states. These physical states carry energy-momentum charges which are divergenceless and obey a deformed dispersion relation.

hep-th↗

arXiv2007

Towards understanding broad degeneracy in non-strange mesons

The spectroscopic regularities of modern empirical data on the non-strange mesons up to 2.4 GeV can be summarized as a systematic clustering of states near certain values of energy. It is getting evident that some unknown X-symmetry triggers the phenomenon. We review the experimental status of this symmetry and recent theoretical attempts put forward for explanation of broad degeneracy.

hep-ph↗

arXiv2007

Symplectic geometry and Noether charges for Hopf algebra space-time symmetries

There has been a certain interest in some recent works in the derivation of Noether charges for Hopf-algebra space-time symmetries. Such analyses relied rather heavily on delicate manipulations of the fields of non-commuting coordinates whose charges were under study. Here we derive the same charges in a "coordinate-independent" symplectic-geometry type of approach and find results that are consistent with the ones of hep-th/0607221.

hep-th↗

arXiv2006

From spacetime foam to holographic foam cosmology

Due to quantum fluctuations, spacetime is foamy on small scales. For maximum spatial resolution of the geometry of spacetime, the holographic model of spacetime foam stipulates that the uncertainty or fluctuation of distance $l$ is given, on the average, by $(l l_P^2)^{1/3}$ where $l_P$ is the Planck length. Applied to cosmology, it predicts that the cosmic energy is of critical density and the cosmic entropy is the maximum allowed by the holographic principle. In addition, it requires the existence of unconventional (dark) energy/matter and accelerating cosmic expansion in the present era. We will argue that a holographic foam cosmology of this type has the potential to become a full fledged competitor (with distinct testable consequences) for scalar driven inflation.

gr-qc↗

arXiv2005

Black hole entropy, log corrections and quantum ergosphere

Quantum-gravity corrections to the probability of emission of a particle from a black hole in the Parikh-Wilczek tunneling framework are studied. We consider the effects of zero-point quantum fluctuations of the metric on the emission probability for a tunneling shell. Quantum properties of the geometry are responsible for the formation of a "quantum egosphere" whose effects on the emission probability can be related to the emergence of a logarithmic correction to the Bekenstein-Hawking entropy-area formula.

gr-qc↗

arXiv2005

Hawking Radiation as Tunneling through the Quantum Horizon

Planck-scale corrections to the black-hole radiation spectrum in the Parikh-Wilczek tunneling framework are calculated. The corrective terms arise from modifications in the expression of the surface gravity in terms of the mass-energy of the black hole-emitted particle system. The form of the new spectrum is discussed together with the possible consequences for the fate of black holes in the late stages of evaporation.

hep-th↗

arXiv2005

Black-hole thermodynamics with modified dispersion relations and generalized uncertainty principles

In several approaches to the quantum-gravity problem evidence has emerged of the validity of a "GUP" (a Generalized position-momentum Uncertainty Principle) and/or a "MDR" (a modification of the energy-momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or a MDR and the possibility of a log term in the area-entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the "Generalized Second Law of black-hole thermodynamics" in theories with a GUP and/or a MDR. After an analysis of GUP- and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.

gr-qc↗

arXiv2005

A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

An insightful argument for a linear relation between the entropy and the area of a black hole was given by Bekenstein using only the energy-momentum dispersion relation, the uncertainty principle, and some properties of classical black holes. Recent analyses within String Theory and Loop Quantum Gravity describe black-hole entropy in terms of a dominant contribution, which indeed depends linearly on the area, and a leading log-area correction. We argue that, by reversing the Bekenstein argument, the log-area correction can provide insight on the energy-momentum dispersion relation and the uncertainty principle of a quantum-gravity theory. As examples we consider the energy-momentum dispersion relations that recently emerged in the Loop Quantum Gravity literature and the Generalized Uncertainty Principle that is expected to hold in String Theory.

hep-th↗

arXiv2005

Tunneling through the quantum horizon

The emergence of quantum-gravity induced corrective terms for the probability of emission of a particle from a black hole in the Parikh-Wilczek tunneling framework is studied. It is shown, in particular, how corrections might arise from modifications of the surface gravity due to near horizon Planck-scale effects. Our derivation provides an example of the possible linking between Planck-scale departures from Lorentz invariance and the appearance of higher order quantum gravity corrections in the black-hole entropy-area relation.

hep-th↗