1,666 research outputs found
Note on Self-Duality and the Kodama State
An interesting interplay between self-duality, the Kodama (Chern-Simons)
state and knot invariants is shown to emerge in the quantum theory of an
Abelian gauge theory. More precisely, when a self-dual representation of the
CCR is chosen, the corresponding vacuum in the Schroedinger representation is
precisely given by the Kodama state. Several consequences of this construction
are explored.Comment: 4 pages, no figures. References and discussion added. Final version
to appear in PR
SU(2) Poisson-Lie T duality
Poisson-Lie target space duality is a framework where duality transformations
are properly defined. In this letter we investigate the pair of sigma models
defined by the double SO(3,1) in the Iwasawa decomposition.Comment: 12 pages, 1 figur
On the deformation quantization of affine algebraic varieties
We compute an explicit algebraic deformation quantization for an affine
Poisson variety described by an ideal in a polynomial ring, and inheriting its
Poisson structure from the ambient space.Comment: AMS-LaTeX, 20 page
Information is Not Lost in the Evaporation of 2-dimensional Black Holes
We analyze Hawking evaporation of the Callen-Giddings-Harvey-Strominger
(CGHS) black holes from a quantum geometry perspective and show that
information is not lost, primarily because the quantum space-time is
sufficiently larger than the classical. Using suitable approximations to
extract physics from quantum space-times we establish that: i)future null
infinity of the quantum space-time is sufficiently long for the the past vacuum
to evolve to a pure state in the future; ii) this state has a finite norm in
the future Fock space; and iii) all the information comes out at future
infinity; there are no remnants.Comment: 4 pages, 2 figure
Deformation Quantization of Coadjoint Orbits
A method for the deformation quantization of coadjoint orbits of semisimple
Lie groups is proposed. It is based on the algebraic structure of the orbit.
Its relation to geometric quantization and differentiable deformations is
explored.Comment: Talk presented at the meeting "Noncommutative geometry and Hopf
algebras in Field Theory and Particle Physics", Torino, 199
Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
We perform a canonical analysis of the system of 2d vacuum dilatonic black
holes. Our basic variables are closely tied to the spacetime geometry and we do
not make the field redefinitions which have been made by other authors. We
present a careful discssion of asymptotics in this canonical formalism.
Canonical transformations are made to variables which (on shell) have a clear
spacetime significance. We are able to deduce the location of the horizon on
the spatial slice (on shell) from the vanishing of a combination of canonical
data. The constraints dramatically simplify in terms of the new canonical
variables and quantization is easy. The physical interpretation of the variable
conjugate to the ADM mass is clarified. This work closely parallels that done
by Kucha{\v r} for the vacuum Schwarzschild black holes and is a starting point
for a similar analysis, now in progress, for the case of a massless scalar
field conformally coupled to a 2d dilatonic black hole.Comment: 21 pages, latex fil
Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles
It is well known that the category of super Lie groups (SLG) is equivalent to
the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we
define the category of unitary representations (UR's) of a super Lie group. We
give an extension of the classical inducing construction and Mackey
imprimitivity theorem to this setting. We use our results to classify the
irreducible unitary representations of semidirect products of super translation
groups by classical Lie groups, in particular of the super Poincar\'e groups in
arbitrary dimension. Finally we compare our results with those in the physical
literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre
Delign
Gravitons from a loop representation of linearised gravity
Loop quantum gravity is based on a classical formulation of 3+1 gravity in
terms of a real SU(2) connection. Linearization of this classical formulation
about a flat background yields a description of linearised gravity in terms of
a {\em real} connection. A `loop' representation,
in which holonomies of this connection are unitary operators, can be
constructed. These holonomies are not well defined operators in the standard
graviton Fock representation. We generalise our recent work on photons and U(1)
holonomies to show that Fock space gravitons are associated with distributional
states in the loop representation. Our results may
illuminate certain aspects of the much deeper (and as yet unkown,) relation
between gravitons and states in nonperturbative loop quantum gravity.
This work leans heavily on earlier seminal work by Ashtekar, Rovelli and
Smolin (ARS) on the loop representation of linearised gravity using {\em
complex} connections. In the last part of this work, we show that the loop
representation based on the {\em real} connection
also provides a useful kinematic arena in which it is possible to express the
ARS complex connection- based results in the mathematically precise language
currently used in the field.Comment: 23 pages, no figure
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