3,524 research outputs found
Holography as a highly efficient RG flow II: An explicit construction
We complete the reformulation of the holographic correspondence as a
\emph{highly efficient RG flow} that can also determine the UV data in the
field theory in the strong coupling and large limit. We introduce a special
way to define operators at any given scale in terms of appropriate
coarse-grained collective variables, without requiring the use of the
elementary fields. The Wilsonian construction is generalised by promoting the
cut-off to a functional of these collective variables. We impose three criteria
to determine the coarse-graining. The first criterion is that the effective
Ward identities for local conservation of energy, momentum, etc. should
preserve their standard forms, but in new scale-dependent background metric and
sources which are functionals of the effective single trace operators. The
second criterion is that the scale-evolution equations of the operators in the
actual background metric should be state-independent, implying that the
collective variables should not explicitly appear in them. The final criterion
is that the endpoint of the scale-evolution of the RG flow can be transformed
to a fixed point corresponding to familiar non-relativistic equations with a
finite number of parameters, such as incompressible non-relativistic
Navier-Stokes, under a certain universal rescaling of the scale and of the time
coordinate. Using previous work, we explicitly show that in the hydrodynamic
limit each such highly efficient RG flow reproduces a unique classical gravity
theory with precise UV data that satisfy our IR criterion. We obtain the
explicit coarse-graining which reproduces Einstein's equations. In a simple
example, we are also able to compute the beta function. Finally, we show how
our construction can be interpolated with the traditional Wilsonian RG flow at
a suitable scale, and can be used to develop new non-perturbative frameworks
for QCD-like theories.Comment: 1+59 pages; Introduction slightly expanded, Section V on beta
function in highly efficient RG flow added, version accepted in PR
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of
the multiple definition given by Bergmann of the concept of {\it (Bergmann)
observable. This clarification leads to the proposal of a {\it main conjecture}
asserting the existence of i) special Dirac's observables which are also
Bergmann's observables, ii) gauge variables that are coordinate independent
(namely they behave like the tetradic scalar fields of the Newman-Penrose
formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict
connection with the Hamiltonian treatment of the initial value problem in
metric gravity for the class of Christoudoulou -Klainermann space-times, in
which the temporal evolution is ruled by the {\it weak} ADM energy. It is
crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive
and metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose their (nearly unknown) connection
to gauge transformations on-shell; this is expounded in the first paper
(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic
pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate
systems for the 4-dimensional {\it mathematical} manifold, in terms of the
highly non-local degrees of freedom of the gravitational field (its four
independent {\it Dirac observables}), and to realize the {\it physical
individuation} of the points of space-time as {\it point-events} as a
gauge-fixing problem, also associating a non-commutative structure to each
4-coordinate system.Comment: 41 pages, Revtex
Gravity and the Quantum
The goal of this article is to present a broad perspective on quantum gravity
for \emph{non-experts}. After a historical introduction, key physical problems
of quantum gravity are illustrated. While there are a number of interesting and
insightful approaches to address these issues, over the past two decades
sustained progress has primarily occurred in two programs: string theory and
loop quantum gravity. The first program is described in Horowitz's contribution
while my article will focus on the second. The emphasis is on underlying ideas,
conceptual issues and overall status of the program rather than mathematical
details and associated technical subtleties.Comment: A general review of quantum gravity addresed non-experts. To appear
in the special issue `Space-time Hundred Years Later' of NJP; J.Pullin and R.
Price (editors). Typos and an attribution corrected; a clarification added in
section 2.
Loop Quantum Cosmology: A Status Report
The goal of this article is to provide an overview of the current state of
the art in loop quantum cosmology for three sets of audiences: young
researchers interested in entering this area; the quantum gravity community in
general; and, cosmologists who wish to apply loop quantum cosmology to probe
modifications in the standard paradigm of the early universe. An effort has
been made to streamline the material so that, as described at the end of
section I, each of these communities can read only the sections they are most
interested in, without a loss of continuity.Comment: 138 pages, 15 figures. Invited Topical Review, To appear in Classical
and Quantum Gravity. Typos corrected, clarifications and references adde
Heat and Fluctuations from Order to Chaos
The Heat theorem reveals the second law of equilibrium Thermodynamics
(i.e.existence of Entropy) as a manifestation of a general property of
Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as
degrees of freedom systems, {\it i.e.} for simple as well as very
complex systems, and reflecting the Hamiltonian nature of the microscopic
motion. In Nonequilibrium Thermodynamics theorems of comparable generality do
not seem to be available. Yet it is possible to find general, model
independent, properties valid even for simple chaotic systems ({\it i.e.} the
hyperbolic ones), which acquire special interest for large systems: the Chaotic
Hypothesis leads to the Fluctuation Theorem which provides general properties
of certain very large fluctuations and reflects the time-reversal symmetry.
Implications on Fluids and Quantum systems are briefly hinted. The physical
meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation
Theorem is discussed in the context of their interpretation and relevance in
terms of Coarse Grained Partitions of phase space. This review is written
taking some care that each section and appendix is readable either
independently of the rest or with only few cross references.Comment: 1) added comment at the end of Sec. 1 to explain the meaning of the
title (referee request) 2) added comment at the end of Sec. 17 (i.e. appendix
A4) to refer to papers related to the ones already quoted (referee request
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