9,379 research outputs found
The century of the incomplete revolution: searching for general relativistic quantum field theory
In fundamental physics, this has been the century of quantum mechanics and
general relativity. It has also been the century of the long search for a
conceptual framework capable of embracing the astonishing features of the world
that have been revealed by these two ``first pieces of a conceptual
revolution''. I discuss the general requirements on the mathematics and some
specific developments towards the construction of such a framework. Examples of
covariant constructions of (simple) generally relativistic quantum field
theories have been obtained as topological quantum field theories, in
nonperturbative zero-dimensional string theory and its higher dimensional
generalizations, and as spin foam models. A canonical construction of a general
relativistic quantum field theory is provided by loop quantum gravity.
Remarkably, all these diverse approaches have turn out to be related,
suggesting an intriguing general picture of general relativistic quantum
physics.Comment: To appear in the Journal of Mathematical Physics 2000 Special Issu
Physics with nonperturbative quantum gravity: radiation from a quantum black hole
We study quantum gravitational effects on black hole radiation, using loop
quantum gravity. Bekenstein and Mukhanov have recently considered the
modifications caused by quantum gravity on Hawking's thermal black-hole
radiation. Using a simple ansatz for the eigenstates the area, they have
obtained the intriguing result that the quantum properties of geometry affect
the radiation considerably, yielding a definitely non-thermal spectrum. Here,
we replace the simple ansatz employed by Bekenstein and Mukhanov with the
actual eigenstates of the area, computed using the loop representation of
quantum gravity. We derive the emission spectra, using a classic result in
number theory by Hardy and Ramanujan. Disappointingly, we do not recover the
Bekenstein-Mukhanov spectrum, but --effectively-- a Hawking's thermal spectrum.
The Bekenstein-Mukhanov result is therefore likely to be an artefact of the
naive ansatz, rather than a robust result. The result is an example of concrete
(although somewhat disappointing) application of nonperturbative quantum
gravity.Comment: 4 pages, latex-revtex, no figure
OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY
We study a tentative generally covariant quantum field theory, denoted the
T-Theory, as a tool to investigate the consistency of quantum general
relativity. The theory describes the gravitational field and a minimally
coupled scalar field; it is based on the loop representation, and on a certain
number of quantization choices. Four-dimensional diffeomorphism-invariant
quantum transition probabilities can be computed from the theory. We present
the explicit calculation of the transition probability between two volume
eigenstates as an example. We discuss the choices on which the T-theory relies,
and the possibilities of modifying them.Comment: Latex file, 33 page
SL(2,R) model with two Hamiltonian constraints
We describe a simple dynamical model characterized by the presence of two
noncommuting Hamiltonian constraints. This feature mimics the constraint
structure of general relativity, where there is one Hamiltonian constraint
associated with each space point. We solve the classical and quantum dynamics
of the model, which turns out to be governed by an SL(2,R) gauge symmetry,
local in time. In classical theory, we solve the equations of motion, find a
SO(2,2) algebra of Dirac observables, find the gauge transformations for the
Lagrangian and canonical variables and for the Lagrange multipliers. In quantum
theory, we find the physical states, the quantum observables, and the physical
inner product, which is determined by the reality conditions. In addition, we
construct the classical and quantum evolving constants of the system. The model
illustrates how to describe physical gauge-invariant relative evolution when
coordinate time evolution is a gauge.Comment: 9 pages, 1 figure, revised version, to appear in Phys. Rev.
Towards the graviton from spinfoams: the 3d toy model
Recently, a proposal has appeared for the extraction of the 2-point function
of linearised quantum gravity, within the spinfoam formalism. This relies on
the use of a boundary state, which introduces a semi-classical flat geometry on
the boundary. In this paper, we investigate this proposal considering a toy
model in the (Riemannian) 3d case, where the semi-classical limit is better
understood. We show that in this limit the propagation kernel of the model is
the one for the harmonic oscillator. This is at the origin of the expected 1/L
behaviour of the 2-point function. Furthermore, we numerically study the short
scales regime, where deviations from this behaviour occur.Comment: 8 pages, 2 figures; v3 revised versio
A semiclassical tetrahedron
We construct a macroscopic semiclassical state state for a quantum
tetrahedron. The expectation values of the geometrical operators representing
the volume, areas and dihedral angles are peaked around assigned classical
values, with vanishing relative uncertainties.Comment: 10 pages; v2 revised versio
The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
Some components of the graviton two-point function have been recently
computed in the context of loop quantum gravity, using the spinfoam
Barrett-Crane vertex. We complete the calculation of the remaining components.
We find that, under our assumptions, the Barrett-Crane vertex does not yield
the correct long distance limit. We argue that the problem is general and can
be traced to the intertwiner-independence of the Barrett-Crane vertex, and
therefore to the well-known mismatch between the Barrett-Crane formalism and
the standard canonical spin networks. In a companion paper we illustrate the
asymptotic behavior of a vertex amplitude that can correct this difficulty.Comment: 31 page
Yang-Mills analogues of the Immirzi ambiguity
We draw parallels between the recently introduced ``Immirzi ambiguity'' of
the Ashtekar-like formulation of canonical quantum gravity and other
ambiguities that appear in Yang-Mills theories, like the ambiguity. We
also discuss ambiguities in the Maxwell case, and implication for the loop
quantization of these theories.Comment: 5 pages, revtex, no figure
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum
gravity, using the spinfoam formalism, up to some second order terms in the
expansion parameter.Comment: 41 pages, 6 figure
Causality in Spin Foam Models
We compute Teitelboim's causal propagator in the context of canonical loop
quantum gravity. For the Lorentzian signature, we find that the resultant power
series can be expressed as a sum over branched, colored two-surfaces with an
intrinsic causal structure. This leads us to define a general structure which
we call a ``causal spin foam''. We also demonstrate that the causal evolution
models for spin networks fall in the general class of causal spin foams.Comment: 19 pages, LaTeX2e, many eps figure
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