Group Theoretical Quantization of a Phase Space S1xR+S^{1} x R^{+} and the Mass Spectrum of Schwarzschild Black Holes in D Space-Time Dimensions

The symplectic reduction of pure spherically symmetric (Schwarzschild) classical gravity in D space-time dimensions yields a 2-dimensional phase space of observables consisting of the Mass M (>0) and a canonically conjugate (Killing) time variable T. Imposing (mass-dependent) periodic boundary conditions in time on the associated quantum mechanical plane waves which represent the Schwarzschild system in the period just before or during the formation of a black hole, yields an energy spectrum of the hole which realizes the old Bekenstein postulate that the quanta of the horizon A_{D-2} are multiples of a basic area quantum. In the present paper it is shown that the phase space of such a Schwarzschild black hole in D space-time dimensions is symplectomorphic to a symplectic manifold S={(phi in R mod 2 pi, p = A_{D-2} >0)} with the symplectic form d phi wedge d p. As the action of the group SO_+(1,2) on that manifold is transitive, effective and Hamiltonian, it can be used for a group theoretical quantization of the system. The area operator p for the horizon corresponds to the generator of the compact subgroup SO(2) and becomes quantized accordingly: The positive discrete series of the irreducible unitary representations of SO_+(1,2) yields an (horizon) area spectrum proportional k+n, where k = 1,2,... characterizes the representation and n = 0,1,2,... the number of area quanta. If one employs the unitary representations of the universal covering group of SO_+(1,2) the number k can take any fixed positive real value (theta-parameter). The unitary representations of the positive discrete series provide concrete Hilbert spaces for quantum Schwarzschild black holes

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Transition from accelerated to decelerated regimes in JT and CGHS cosmologies

In this work we discuss the possibility of positive-acceleration regimes, and their transition to decelerated regimes, in two-dimensional (2D) cosmological models. We use general relativity and the thermodynamics in a 2D space-time, where the gas is seen as the sources of the gravitational field. An early-Universe model is analyzed where the state equation of van der Waals is used, replacing the usual barotropic equation. We show that this substitution permits the simulation of a period of inflation, followed by a negative-acceleration era. The dynamical behavior of the system follows from the solution of the Jackiw-Teitelboim equations (JT equations) and the energy-momentum conservation laws. In a second stage we focus the Callan-Giddings-Harvey-Strominger model (CGHS model); here the transition from the inflationary period to the decelerated period is also present between the solutions, although this result depend strongly on the initial conditions used for the dilaton field. The temporal evolution of the cosmic scale function, its acceleration, the energy density and the hydrostatic pressure are the physical quantities obtained in through the analysis.Comment: To appear in Europhysics Letter

A PHD12–Snail2 repressive complex epigenetically mediates neural crest epithelial-to-mesenchymal transition

Neural crest cells form within the neural tube and then undergo an epithelial to mesenchymal transition (EMT) to initiate migration to distant locations. The transcriptional repressor Snail2 has been implicated in neural crest EMT via an as of yet unknown mechanism. We report that the adaptor protein PHD12 is highly expressed before neural crest EMT. At cranial levels, loss of PHD12 phenocopies Snail2 knockdown, preventing transcriptional shutdown of the adhesion molecule Cad6b (Cadherin6b), thereby inhibiting neural crest emigration. Although not directly binding to each other, PHD12 and Snail2 both directly interact with Sin3A in vivo, which in turn complexes with histone deacetylase (HDAC). Chromatin immunoprecipitation revealed that PHD12 is recruited to the Cad6b promoter during neural crest EMT. Consistent with this, lysines on histone 3 at the Cad6b promoter are hyperacetylated before neural crest emigration, correlating with active transcription, but deacetylated during EMT, reflecting the repressive state. Knockdown of either PHD12 or Snail2 prevents Cad6b promoter deacetylation. Collectively, the results show that PHD12 interacts directly with Sin3A/HDAC, which in turn interacts with Snail2, forming a complex at the Cad6b promoter and thus revealing the nature of the in vivo Snail repressive complex that regulates neural crest EMT

Nuclear magnetic resonance measurements reveal the origin of the Debye process in monohydroxy alcohols

Monohydroxy alcohols show a structural relaxation and at longer time scales a Debye-type dielectric peak. From spin-lattice relaxation experiments using different nuclear probes an intermediate, slower-than-structural dynamics is identified for n-butanol. Based on these findings and on diffusion measurements, a model of self-restructuring, transient chains is proposed. The model is demonstrated to explain consistently the so far puzzling observations made for this class of hydrogen-bonded glass forming liquids.Comment: 4 pages, 4 figure

Exact Path Integral Quantization of Generic 2-D Dilaton Gravity

Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present.Comment: 15 page

DNA methyltransferase 3B regulates duration of neural crest production via repression of Sox10

Neural crest stem cells arise within the central nervous system but then undergo an epithelial-to-mesenchymal transition to migrate away and contribute to the peripheral nervous system and craniofacial skeleton. Here we show that DNA methyltransferase 3B (DNMT3B) is responsible for the loss of competence of dorsal neural tube cells to generate emigrating neural crest cells. DNMT3B knockdown results in up-regulation of neural crest markers, prolonged neural crest emigration, and subsequent precocious neuronal differentiation of the trigeminal ganglion. We find that DNMT3B binds to the promoter of Sox10, known to be important for neural crest emigration and lineage acquisition. Bisulfite sequencing further reveals methylation of the Sox10 promoter region upon cessation of emigration in normal embryos, whereas this mark is reduced after DNMT3B loss. Taken together, these results reveal the importance of DNA methylation in regulating the ability of neural tube cells to produce neural crest cells and the timing of peripheral neuron differentiation

A path integral approach to the dynamics of a random chain with rigid constraints

In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain.Comment: 36 pages, 2 figures, LaTeX + REVTeX4 + graphicx, minor changes in the text, reference adde

Generalized 2d dilaton gravity with matter fields

We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we provide the complete solution of the most general dilaton-dependent 2d gravity action coupled to chiral fermions. The latter analysis is generalized to a chiral fermion multiplet with a non-abelian gauge symmetry as well as to the (anti-)self-dual sector df = *df (df = -*df) of a scalar field f.Comment: 37 pages, Latex; typos and Eqs. (44,45) corrected; paragraph on p. 26, referring to a work of S. Solodukhin, reformulated; references adde