1,697 research outputs found
Non-minimal couplings, quantum geometry and black hole entropy
The black hole entropy calculation for type I isolated horizons, based on
loop quantum gravity, is extended to include non-minimally coupled scalar
fields. Although the non-minimal coupling significantly modifies quantum
geometry, the highly non-trivial consistency checks for the emergence of a
coherent description of the quantum horizon continue to be met. The resulting
expression of black hole entropy now depends also on the scalar field precisely
in the fashion predicted by the first law in the classical theory (with the
same value of the Barbero-Immirzi parameter as in the case of minimal
coupling).Comment: 14 pages, no figures, revtex4. Section III expanded and typos
correcte
2+1 Gravity without dynamics
A three dimensional generally covariant theory is described that has a 2+1
canonical decomposition in which the Hamiltonian constraint, which generates
the dynamics, is absent. Physical observables for the theory are described and
the classical and quantum theories are compared with ordinary 2+1 gravity.Comment: 9 page
Photon inner product and the Gauss linking number
It is shown that there is an interesting interplay between self-duality, loop
representation and knots invariants in the quantum theory of Maxwell fields in
Minkowski space-time. Specifically, in the loop representation based on
self-dual connections, the measure that dictates the inner product can be
expressed as the Gauss linking number of thickened loops.Comment: 18 pages, Revtex. No figures. To appear in Class. Quantum Gra
Fock representations from U(1) holonomy algebras
We revisit the quantization of U(1) holonomy algebras using the abelian C*
algebra based techniques which form the mathematical underpinnings of current
efforts to construct loop quantum gravity. In particular, we clarify the role
of ``smeared loops'' and of Poincare invariance in the construction of Fock
representations of these algebras. This enables us to critically re-examine
early pioneering efforts to construct Fock space representations of linearised
gravity and free Maxwell theory from holonomy algebras through an application
of the (then current) techniques of loop quantum gravity.Comment: Latex file, 30 pages, to appear in Phys Rev
Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context
Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian)
Hamiltonian quantum theory starting from a measure on the space of (Euclidean)
histories of a scalar quantum field. In this paper, we extend that construction
to more general theories which do not refer to any background, space-time
metric (and in which the space of histories does not admit a natural linear
structure). Examples include certain gauge theories, topological field theories
and relativistic gravitational theories. The treatment is self-contained in the
sense that an a priori knowledge of the Osterwalder-Schrader theorem is not
assumed.Comment: Plain Latex, 25 p., references added, abstract and title changed
(originally :``Osterwalder Schrader Reconstruction and Diffeomorphism
Invariance''), introduction extended, one appendix with illustrative model
added, accepted by Class. Quantum Gra
Gauss Linking Number and Electro-magnetic Uncertainty Principle
It is shown that there is a precise sense in which the Heisenberg uncertainty
between fluxes of electric and magnetic fields through finite surfaces is given
by (one-half times) the Gauss linking number of the loops that bound
these surfaces. To regularize the relevant operators, one is naturally led to
assign a framing to each loop. The uncertainty between the fluxes of electric
and magnetic fields through a single surface is then given by the self-linking
number of the framed loop which bounds the surface.Comment: 13 pages, Revtex file, 3 eps figure
Quantum horizons and black hole entropy: Inclusion of distortion and rotation
Equilibrium states of black holes can be modelled by isolated horizons. If
the intrinsic geometry is spherical, they are called type I while if it is
axi-symmetric, they are called type II. The detailed theory of geometry of
\emph{quantum} type I horizons and the calculation of their entropy can be
generalized to type II, thereby including arbitrary distortions and rotations.
The leading term in entropy of large horizons is again given by 1/4th of the
horizon area for the \emph{same} value of the Barbero-Immirzi parameter as in
the type I case. Ideas and constructions underlying this extension are
summarized.Comment: 9 page
Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
Analytical and numerical methods are developed to analyze the quantum nature
of the big bang in the setting of loop quantum cosmology. They enable one to
explore the effects of quantum geometry both on the gravitational and matter
sectors and significantly extend the known results on the resolution of the big
bang singularity. Specifically, the following results are established for the
homogeneous isotropic model with a massless scalar field: i) the scalar field
is shown to serve as an internal clock, thereby providing a detailed
realization of the `emergent time' idea; ii) the physical Hilbert space, Dirac
observables and semi-classical states are constructed rigorously; iii) the
Hamiltonian constraint is solved numerically to show that the big bang is
replaced by a big bounce. Thanks to the non-perturbative, background
independent methods, unlike in other approaches the quantum evolution is
deterministic across the deep Planck regime. Our constructions also provide a
conceptual framework and technical tools which can be used in more general
models. In this sense, they provide foundations for analyzing physical issues
associated with the Planck regime of loop quantum cosmology as a whole.Comment: Revised version to appear in Physical Review D. References added and
typos correcte
Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology
In this paper we review a model based on loop quantum cosmology that arises
from a symmetry reduction of the self dual Plebanski action. In this
formulation the symmetry reduction leads to a very simple Hamiltonian
constraint that can be quantized explicitly in the framework of loop quantum
cosmology. We investigate the phenomenological implications of this model in
the semi-classical regime and compare those with the known results of the
standard Loop Quantum Cosmology.Comment: 10 pages, 7 figure
Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
Loop quantum gravity is an approach to quantum gravity that starts from the
Hamiltonian formulation in terms of a connection and its canonical conjugate.
Quantization proceeds in the spirit of Dirac: First one defines an algebra of
basic kinematical observables and represents it through operators on a suitable
Hilbert space. In a second step, one implements the constraints. The main
result of the paper concerns the representation theory of the kinematical
algebra: We show that there is only one cyclic representation invariant under
spatial diffeomorphisms.
While this result is particularly important for loop quantum gravity, we are
rather general: The precise definition of the abstract *-algebra of the basic
kinematical observables we give could be used for any theory in which the
configuration variable is a connection with a compact structure group. The
variables are constructed from the holonomy map and from the fluxes of the
momentum conjugate to the connection. The uniqueness result is relevant for any
such theory invariant under spatial diffeomorphisms or being a part of a
diffeomorphism invariant theory.Comment: 38 pages, one figure. v2: Minor changes, final version, as published
in CM
- …