1,034 research outputs found
Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
Quantum gravity is studied nonperturbatively in the case in which space has a
boundary with finite area. A natural set of boundary conditions is studied in
the Euclidean signature theory, in which the pullback of the curvature to the
boundary is self-dual (with a cosmological constant). A Hilbert space which
describes all the information accessible by measuring the metric and connection
induced in the boundary is constructed and is found to be the direct sum of the
state spaces of all Chern-Simon theories defined by all choices of
punctures and representations on the spatial boundary . The integer
level of Chern-Simons theory is found to be given by , where is the cosmological constant and is a
breaking phase. Using these results, expectation values of observables which
are functions of fields on the boundary may be evaluated in closed form. The
Beckenstein bound and 't Hooft-Susskind holographic hypothesis are confirmed,
(in the limit of large area and small cosmological constant) in the sense that
once the two metric of the boundary has been measured, the subspace of the
physical state space that describes the further information that the observer
on the boundary may obtain about the interior has finite dimension equal to the
exponent of the area of the boundary, in Planck units, times a fixed constant.
Finally,the construction of the state space for quantum gravity in a region
from that of all Chern-Simon theories defined on its boundary confirms the
categorical-theoretic ``ladder of dimensions picture" of Crane.Comment: TEX File, Minor Changes Made, 59 page
The linearization of the Kodama state
We study the question of whether the linearization of the Kodama state around
classical deSitter spacetime is normalizable in the inner product of the theory
of linearized gravitons on deSitter spacetime. We find the answer is no in the
Lorentzian theory. However, in the Euclidean theory the corresponding
linearized Kodama state is delta-functional normalizable. We discuss whether
this result invalidates the conjecture that the full Kodama state is a good
physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte
Self-organized critical behavior: the evolution of frozen spin networks model in quantum gravity
In quantum gravity, we study the evolution of a two-dimensional planar open
frozen spin network, in which the color (i.e. the twice spin of an edge)
labeling edge changes but the underlying graph remains fixed. The mainly
considered evolution rule, the random edge model, is depending on choosing an
edge randomly and changing the color of it by an even integer. Since the change
of color generally violate the gauge invariance conditions imposed on the
system, detailed propagation rule is needed and it can be defined in many ways.
Here, we provided one new propagation rule, in which the involved even integer
is not a constant one as in previous works, but changeable with certain
probability. In random edge model, we do find the evolution of the system under
the propagation rule exhibits power-law behavior, which is suggestive of the
self-organized criticality (SOC), and it is the first time to verify the SOC
behavior in such evolution model for the frozen spin network. Furthermore, the
increase of the average color of the spin network in time can show the nature
of inflation for the universe.Comment: 5 pages, 5 figure
Mixmaster quantum cosmology in terms of physical dynamics
An approach to quantum cosmology, relying on strengths of both canonical and path integral formalisms, is applied to the cosmological model, Bianchi type IX. Physical quantum states are constructed on the maximal slice of the cosmological history. A path integral is derived which evolves observables off the maximal slice. This result is compared a path integral propagator derived earlier with conventional Faddeev-Poppov gauge fixing
Quantum Gravity as a Deformed Topological Quantum Field Theory
It is known that the Einstein-Hilbert action with a positive cosmological
constant can be represented as a perturbation of the SO(4,1) BF theory by a
symmetry-breaking term quadratic in the B field. Introducing fermionic matter
generates additional terms in the action which are polynomial in the tetrads
and the spin connection. We describe how to construct the generating functional
in the spin foam formalism for a generic BF theory when the sources for the B
and the gauge field are present. This functional can be used to obtain a path
integral for General Relativity with matter as a perturbative series whose the
lowest order term is a path integral for a topological gravity coupled to
matter.Comment: 7 pages, talk presented at the QG05 conference, 12-16 September 2005,
Cala Gonone, Ital
On the Hamiltonian Constraint of Loop Quantum Cosmology
In this paper we construct the Hamiltonian constraint operator of loop
quantum cosmology using holonomies defined for arbitrary irreducible SU(2)
representations labeled by spin J. We show that modifications to the effective
semi-classical equations of motion arise both in the gravitational part of the
constraint as well as matter terms. The modifications are important for
phenomenological investigations of the cosmological imprints of loop quantum
cosmology. We discuss the implications for the early universe evolution
Relative Locality in -Poincar\'e
We show that the -Poincar\'e Hopf algebra can be interpreted in the
framework of curved momentum space leading to the relativity of locality
\cite{AFKS}. We study the geometric properties of the momentum space described
by -Poincar\'e, and derive the consequences for particles propagation
and energy-momentum conservation laws in interaction vertices, obtaining for
the first time a coherent and fully workable model of the deformed relativistic
kinematics implied by -Poincar\'e. We describe the action of boost
transformations on multi-particles systems, showing that in order to keep
covariant the composed momenta it is necessary to introduce a dependence of the
rapidity parameter on the particles momenta themselves. Finally, we show that
this particular form of the boost transformations keeps the validity of the
relativity principle, demonstrating the invariance of the equations of motion
under boost transformations.Comment: 24 pages, 4 figures, 1 table. v2 matches accepted CQG versio
Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model
In this paper we construct the generalized Kodama state for the case of a
Klein--Gordon scalar field coupled to Ashtekar variables in isotropic
minisuperspace by a new method. The criterion for finiteness of the state stems
from a minisuperspace reduction of the quantized full theory, rather than the
conventional techniques of reduction prior to quantization. We then provide a
possible route to the reproduction of a semiclassical limit via these states.
This is the result of a new principle of the semiclassical-quantum
correspondence (SQC), introduced in the first paper in this series. Lastly, we
examine the solution to the minisuperspace case at the semiclassical level for
an isotropic CDJ matrix neglecting any quantum corrections and examine some of
the implications in relation to results from previous authors on semiclassical
orbits of spacetime, including inflation. It is suggested that the application
of nonperturbative quantum gravity, by way of the SQC, might potentially lead
to some predictions testable below the Planck scale.Comment: 26 pages. Accepted for publication by Class. Quantum Grav. journa
Link Invariants of Finite Type and Perturbation Theory
The Vassiliev-Gusarov link invariants of finite type are known to be closely
related to perturbation theory for Chern-Simons theory. In order to clarify the
perturbative nature of such link invariants, we introduce an algebra V_infinity
containing elements g_i satisfying the usual braid group relations and elements
a_i satisfying g_i - g_i^{-1} = epsilon a_i, where epsilon is a formal variable
that may be regarded as measuring the failure of g_i^2 to equal 1.
Topologically, the elements a_i signify crossings. We show that a large class
of link invariants of finite type are in one-to-one correspondence with
homogeneous Markov traces on V_infinity. We sketch a possible application of
link invariants of finite type to a manifestly diffeomorphism-invariant
perturbation theory for quantum gravity in the loop representation.Comment: 11 page
Simulating quantum operations with mixed environments
We study the physical resources required to implement general quantum
operations, and provide new bounds on the minimum possible size which an
environment must be in order to perform certain quantum operations. We prove
that contrary to a previous conjecture, not all quantum operations on a
single-qubit can be implemented with a single-qubit environment, even if that
environment is initially prepared in a mixed state. We show that a mixed
single-qutrit environment is sufficient to implement a special class of
operations, the generalized depolarizing channels.Comment: 4 pages Revtex + 1 fig, pictures at
http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small correction
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