162 research outputs found
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation
We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression
for the finite residual gauge transformations has been worked ou
SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity
We consider a space-time with spatial sections isomorphic to the group
manifold of SU(2). Triad and connection fluctuations are assumed to be
SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform
non-perturbative path integral quantization of the model. Contarary to previous
claims the path integral measure appeared to be non-singular near
configurations admitting additional Killing vectors. In this model we are able
to calculate the generating functional of Green functions of the reduced phase
space variables exactly.Comment: 12 page
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
Constants of motion for vacuum general relativity
The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting
spacelike Killing vector fields, may be written as the equations of the
principal chiral model with certain `source' terms. Using this
formulation, we give a procedure for generating an infinite number of non-local
constants of motion for this sector of the Einstein equations. The constants of
motion arise as explicit functionals on the phase space of Einstein gravity,
and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D
Iatrogenic panhypopituitarism: how many puzzles you need to solve on your way to pregnancy: a clinical case
Introduction. Iatrogenic panhypopituitarism requires specific approaches to infertility treatment, prenatal care and childbearing. Aim: to show difficulties and peculiarities of infertility treatment of a patient with iatrogenic panhypopituitarism. Methods and materials. We present a clinical case of an infertile patient with panhypopituitarism followed the operation for a chromophobe pituitary adenoma. Results. The 31-year old infertile patient was operated at the age of 21 for pituitary adenoma, the surgery was followed by the hormone replacement therapy. At examination: Anti-Mullerian hormone - 0,28 ng/mL., uterine hypoplasia by ultrasound, hysterosalpingography showed that fallopian tubes were passable, normospermia. Three ovulation stimulations were performed: the first one - Menopur®, the "step up" protocol (after 44-day period one dominant follicle developed); the second - Menopur® "step up" (after 26-day period 4 follicles developed), both times - biochemical pregnancy; the third stimulation - 20 days using Gonal-F® 150 ME and Pregnyl 70 M.E., 4 follicles developed, childbirth went after pregnancy. During the stimulation, growth hormone, cortisol and low molecular weight heparin were added, with the extension of the growth hormone administration to the 36th week of gestation. Conclusion. Patients with hypogonadotropic hypogonadism are a population in which ovulation stimulation leads to folliculogenesis in 80 % of cases. The following questions remain debatable: Is the corresponding function achieved when solving the problem of uterine hypoplasia? Should we add growth hormone and for how long? How to evaluate the follicular reserve, and is Anti-Mullerian hormone accurate in such patients? What is the best compensation for luteinizing hormone activity? Is human chorionic gonadotropin the key to pregnancy
Functional evolution of quantum cylindrical waves
Kucha{\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical
wave solutions to vacuum general relativity is determined by that of a free
axially-symmetric scalar field along arbitrary axially-symmetric foliations of
a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can
be defined {\em unitarily} within the standard Fock space quantization of the
scalar field.
Evolution between two arbitrary slices of an arbitrary foliation of the flat
spacetime can be built out of a restricted class of evolutions (and their
inverses). The restricted evolution is from an initial flat slice to an
arbitrary (in general, curved) slice of the flat spacetime and can be
decomposed into (i) `time' evolution in which the spatial Minkowskian
coordinates serve as spatial coordinates on the initial and the final slice,
followed by (ii) the action of a spatial diffeomorphism of the final slice on
the data obtained from (i). We show that although the functional evolution of
(i) is unitarily implemented in the quantum theory, generic spatial
diffeomorphisms of (ii) are not. Our results imply that a Tomanaga-Schwinger
type functional evolution of quantum cylindrical waves is not a viable concept
even though, remarkably, the more limited notion of functional evolution in
Kucha{\v{r}}'s `half parametrized formalism' is well-defined.Comment: Replaced with published versio
Asymptotic behaviour of cylindrical waves interacting with spinning strings
We consider a family of cylindrical spacetimes endowed with angular momentum
that are solutions to the vacuum Einstein equations outside the symmetry axis.
This family was recently obtained by performing a complete gauge fixing adapted
to cylindrical symmetry. In the present work, we find boundary conditions that
ensure that the metric arising from this gauge fixing is well defined and that
the resulting reduced system has a consistent Hamiltonian dynamics. These
boundary conditions must be imposed both on the symmetry axis and in the region
far from the axis at spacelike infinity. Employing such conditions, we
determine the asymptotic behaviour of the metric close to and far from the
axis. In each of these regions, the approximate metric describes a conical
geometry with a time dislocation. In particular, around the symmetry axis the
effect of the singularity consists in inducing a constant deficit angle and a
timelike helical structure. Based on these results and on the fact that the
degrees of freedom in our family of metrics coincide with those of cylindrical
vacuum gravity, we argue that the analysed set of spacetimes represent
cylindrical gravitational waves surrounding a spinning cosmic string. For any
of these spacetimes, a prediction of our analysis is that the wave content
increases the deficit angle at spatial infinity with respect to that detected
around the axis.Comment: 25 pages, accepted for publication in Classical and Quantum Gravit
Non-crystallographic reduction of generalized Calogero-Moser models
We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero–Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic types, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models, how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
Einstein's equations and the chiral model
The vacuum Einstein equations for spacetimes with two commuting spacelike
Killing field symmetries are studied using the Ashtekar variables. The case of
compact spacelike hypersurfaces which are three-tori is considered, and the
determinant of the Killing two-torus metric is chosen as the time gauge. The
Hamiltonian evolution equations in this gauge may be rewritten as those of a
modified SL(2) principal chiral model with a time dependent `coupling
constant', or equivalently, with time dependent SL(2) structure constants. The
evolution equations have a generalized zero-curvature formulation. Using this
form, the explicit time dependence of an infinite number of
spatial-diffeomorphism invariant phase space functionals is extracted, and it
is shown that these are observables in the sense that they Poisson commute with
the reduced Hamiltonian. An infinite set of observables that have SL(2) indices
are also found. This determination of the explicit time dependence of an
infinite set of spatial-diffeomorphism invariant observables amounts to the
solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.
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