1,271 research outputs found
The Extended Loop Representation of Quantum Gravity
A new representation of Quantum Gravity is developed. This formulation is
based on an extension of the group of loops. The enlarged group, that we call
the Extended Loop Group, behaves locally as an infinite dimensional Lie group.
Quantum Gravity can be realized on the state space of extended loop dependent
wavefunctions. The extended representation generalizes the loop representation
and contains this representation as a particular case. The resulting
diffeomorphism and hamiltonian constraints take a very simple form and allow to
apply functional methods and simplify the loop calculus. In particular we show
that the constraints are linear in the momenta. The nondegenerate solutions
known in the loop representation are also solutions of the constraints in the
new representation. The practical calculation advantages allows to find a new
solution to the Wheeler-DeWitt equation. Moreover, the extended representation
puts in a precise framework some of the regularization problems of the loop
representation. We show that the solutions are generalized knot invariants,
smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1
Extended Loops: A New Arena for Nonperturbative Quantum Gravity
We propose a new representation for gauge theories and quantum gravity. It
can be viewed as a generalization of the loop representation. We make use of a
recently introduced extension of the group of loops into a Lie Group. This
extension allows the use of functional methods to solve the constraint
equations. It puts in a precise framework the regularization problems of the
loop representation. It has practical advantages in the search for quantum
states. We present new solutions to the Wheeler-DeWitt equation that reinforce
the conjecture that the Jones Polynomial is a state of nonperturbative quantum
gravity.Comment: 12pp, Revtex, no figures, CGPG-93/12-
Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold
Given a Riemannian manifold M and a hypersurface H in M, it is well known
that infinitesimal convexity on a neighborhood of a point in H implies local
convexity. We show in this note that the same result holds in a semi-Riemannian
manifold. We make some remarks for the case when only timelike, null or
spacelike geodesics are involved. The notion of geometric convexity is also
reviewed and some applications to geodesic connectedness of an open subset of a
Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference
and several comments, statement of last proposition correcte
Forster energy transfer signatures in optically driven quantum dot molecules
The Forster resonant energy transfer mechanism (FRET) is investigated in
optically driven and electrically gated tunnel coupled quantum dot molecules.
Two novel FRET induced optical signatures are found in the dressed excitonic
spectrum. This is constructed from exciton level occupation as function of pump
laser energy and applied bias, resembling a level anticrossing spectroscopy
measurement. We observe a redistribution of spectral weight and splitting of
the exciton spectral lines. FRET among single excitons induces a splitting in
the spatially-direct exciton lines, away from the anticrossing due to charge
tunneling in the molecule. However, near the anticrossing, a novel signature
appears as a weak satellite line following an indirect exciton line. FRET
signatures may also occur among indirect excitons, appearing as split indirect
lines. In that case, the signatures appear also in the direct biexciton states,
as the indirect satellite mixes in near the tunneling anticrossing region
Gauge invariant Boltzmann equation and the fluid limit
This article investigates the collisionless Boltzmann equation up to second
order in the cosmological perturbations. It describes the gauge dependence of
the distribution function and the construction of a gauge invariant
distribution function and brightness, and then derives the gauge invariant
fluid limit.Comment: 36 page
A new approach to cosmological perturbations in f(R) models
We propose an analytic procedure that allows to determine quantitatively the
deviation in the behavior of cosmological perturbations between a given f(R)
modified gravity model and a LCDM reference model. Our method allows to study
structure formation in these models from the largest scales, of the order of
the Hubble horizon, down to scales deeply inside the Hubble radius, without
employing the so-called "quasi-static" approximation. Although we restrict our
analysis here to linear perturbations, our technique is completely general and
can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's
suggestions; Typos corrected; Added Reference
Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum
We perform the analysis of the trispectrum of curvature perturbations
generated by the interactions characterizing a general theory of single-field
inflation obtained by effective field theory methods. We find that
curvature-generated interaction terms, which can in general give an important
contribution to the amplitude of the four-point function, show some new
distinctive features in the form of their trispectrum shape-function. These
interesting interactions are invariant under some recently proposed symmetries
of the general theory and, as shown explicitly, do allow for a large value of
the trispectrum.Comment: 29 pages, 13 figure
CMB 3-point functions generated by non-linearities at recombination
We study the 3-point functions generated at recombination in the squeezed
triangle limit, when one mode has a wavelength much larger than the other two
and is outside the horizon. The presence of the long wavelength mode cannot
change the physics inside the horizon but modifies how a late time observer
sees the anisotropies. The effect of the long wavelength mode can be divided
into a redefinition of time and spatial scales, a Shapiro time delay and
gravitational lensing. The separation is gauge dependent but helps develop
intuition. We show that the resulting 3-point function corresponds to an f_NL <
1 and that its shape is different from that created by the f_NL (or local)
model.Comment: 16 pages, 4 figures. Expanded introduction of sec.2. Published
versio
Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum
The methods of effective field theory are used to study generic theories of
inflation with a single inflaton field and to perform a general analysis of the
associated non-Gaussianities. We investigate the amplitudes and shapes of the
various generic three-point correlators, the bispectra, which may be generated
by different classes of single-field inflationary models. Besides the
well-known results for the DBI-like models and the ghost inflationary theories,
we point out that curvature-related interactions may give rise to large
non-Gaussianities in the form of bispectra characterized by a flat shape which,
quite interestingly, is independently produced by several interaction terms. In
a subsequent work, we will perform a similar general analysis for the
non-Gaussianities generated by the generic four-point correlator, the
trispectrum.Comment: Version matching the one published in JCAP, 2 typos fixed, references
added. 30 pages, 20 figure
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