313 research outputs found
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
We present an introduction to the canonical quantization of gravity performed
in loop quantum gravity, based on lectures held at the 3rd quantum geometry and
quantum gravity school in Zakopane in 2011. A special feature of this
introduction is the inclusion of new proposals for coupling matter to gravity
that can be used to deparametrize the theory, thus making its dynamics more
tractable. The classical and quantum aspects of these new proposals are
explained alongside the standard quantization of vacuum general relativity in
loop quantum gravity.Comment: 56 pages. Contribution to the Proceedings of the 3rd Quantum Geometry
and Quantum Gravity School in Zakopane (2011). v2: Typos corrected, various
small changes in presentation, version as published in Po
Regularity of conjugacies of linearizable generalized interval exchange transformations
We consider generalized interval exchange transformations (GIETs) of d
intervals () which are linearizable, i.e. differentiably conjugated to
standard interval exchange maps (IETs) via a diffeomorphism h of [0, 1] and
study the regularity of the conjugacy h. Using a renormalisation operator
obtained accelerating Rauzy-Veech induction, we show that, under a full measure
condition on the IET obtained by linearization, if the orbit of the GIET under
renormalisation converges exponentially fast in a distance to the
subspace of IETs, there exists an exponent such that h is
. Combined with the results proved by the authors in [4], this
implies in particular the following improvement of the rigidity result in genus
two proved in previous work by the same authors (from to
rigidity): for almost every irreducible IET with d = 4 or d = 5, for any
GIET which is topologically conjugate to via a homeomorphism h and has
vanishing boundary, the topological conjugacy h is actually a
diffeomorphism, i.e. a diffeomorphism h with derivative Dh which is
-H\"older continuous.Comment: 28 pages, 4 figure
Singularities of plane complex curves and limits of K\"ahler metrics with cone singularities. I: Tangent Cones
We construct and classify, in the case of two complex dimensions, the
possible tangent cones at points of limit spaces of non-collapsed sequences of
K\"ahler-Einstein metrics with cone singularities.Comment: Reference to Panov's Polyhedral Kahler Manifolds adde
Deformed Lorentz Symmetry and High-Energy Astrophysics (I)
An updated discussion of Lorentz symmetry violation in particle physics at
very high energy is presented, focusing on applications of models of deformed
Lorentz symmetry to high-energy astrophysics.Comment: Updated version of a talk given at the ICRC 1999 Conferenc
Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
In this paper, we review two approaches that can describe, in a geometrical
way, the kinematics of particles that are affected by Planck-scale departures,
named Finsler and Hamilton geometries. By relying on maps that connect the
spaces of velocities and momenta, we discuss the properties of configuration
and phase spaces induced by these two distinct geometries. In particular, we
exemplify this approach by considering the so-called -de Sitter-inspired
modified dispersion relation as a laboratory for this study. We finalize with
some points that we consider as positive and negative ones of each approach for
the description of quantum configuration and phases spaces.Comment: 22 pages. Matches published version. Invited contribution for
Physics. Special Issue "New Advances in Quantum Geometry
Quantum simulation of (1+1)D QED via a Zn lattice Gauge theory
La simulazione di un sistema quantistico complesso rappresenta ancora oggi una sfida estremamente impegnativa a causa degli elevati costi computazionali. La dimensione dello spazio di Hilbert cresce solitamente in modo esponenziale all'aumentare della taglia, rendendo di fatto impossibile una implementazione esatta anche sui più potenti calcolatori. Nel tentativo di superare queste difficoltà , sono stati sviluppati metodi stocastici classici, i quali tuttavia non garantiscono precisione per sistemi fermionici fortemente interagenti o teorie di campo in regimi di densità finita. Di qui, la necessità di un nuovo metodo di simulazione, ovvero la simulazione quantistica. L'idea di base è molto semplice: utilizzare un sistema completamente controllabile, chiamato simulatore quantistico, per analizzarne un altro meno accessibile. Seguendo tale idea, in questo lavoro di tesi si è utilizzata una teoria di gauge discreta con simmetria Zn per una simulazione dell'elettrodinamica quantistica in (1+1)D, studiando alcuni fenomeni di attivo interesse di ricerca, come il diagramma di fase o la dinamica di string-breaking, che generalmente non sono accessibili mediante simulazioni classiche. Si propone un diagramma di fase del modello caratterizzato dalla presenza di una fase confinata, in cui emergono eccitazioni mesoniche ed antimesoniche, cioè stati legati particella-antiparticella, ed una fase deconfinata
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
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