3,059 research outputs found
Compact Lattice QED and the Coulomb Potential
The potential energy of a static charge distribution on a lattice is
rigorously computed in the standard compact quantum electrodynamic model. The
method used follows closely that of Weyl for ordinary quantum electrodynamics
in continuous space-time. The potential energy of the static charge
distribution is independent of temperature and can be calculated from the
lattice version of Poisson's equation. It is the usual Coulomb potential.Comment: 6 pages, includes one figure in Topdrawer, NUB 3054/9
Variational Approach to Gaussian Approximate Coherent States: Quantum Mechanics and Minisuperspace Field Theory
This paper has a dual purpose. One aim is to study the evolution of coherent
states in ordinary quantum mechanics. This is done by means of a Hamiltonian
approach to the evolution of the parameters that define the state. The
stability of the solutions is studied. The second aim is to apply these
techniques to the study of the stability of minisuperspace solutions in field
theory. For a theory we show, both by means of perturbation
theory and rigorously by means of theorems of the K.A.M. type, that the
homogeneous minisuperspace sector is indeed stable for positive values of the
parameters that define the field theory.Comment: 26 pages, Plain TeX, no figure
Inhomogeneous scalar field solutions and inflation
We present new exact cosmological inhomogeneous solutions for gravity coupled
to a scalar field in a general framework specified by the parameter .
The equations of motion (and consequently the solutions) in this framework
correspond either to low-energy string theory or Weyl integrable spacetime
according to the sign of . We show that different inflationary
behaviours are possible, as suggested by the study of the violation of the
strong energy condition. Finally, by the analysis of certain curvature scalars
we found that some of the solutions may be nonsingular.Comment: LaTex file, 14 page
Inflation and Holography in String Theory
The encoding of an inflating patch of space-time in terms of a dual theory is
discussed. Following Bousso's interpretation of the holographic principle, we
find that those are generically described not by states in the dual theory but
by density matrices. We try to implement this idea on simple deformations of
the AdS/CFT examples, and an argument is given as to why inflation is so
elusive to string theory.Comment: 15 pages, LaTeX, 2 figures. Uses psbox.te
Protogalactic Extension of the Parker Bound
We extend the Parker bound on the galactic flux of magnetic
monopoles. By requiring that a small initial seed field must survive the
collapse of the protogalaxy, before any regenerative dynamo effects become
significant, we develop a stronger bound. The survival and continued growth of
an initial galactic seed field G demand that . For a given
monopole mass, this bound is four and a half orders of magnitude more stringent
than the previous `extended Parker bound', but is more speculative as it
depends on assumptions about the behavior of magnetic fields during
protogalactic collapse. For monopoles which do not overclose the Universe
(), the maximum flux allowed is now cm^{-2}
s^{-1} sr^{-1}, a factor of 150 lower than the maximum flux allowed by the
extended Parker bound.Comment: 9 pages, 1 eps figur
Ring Closing Alkyne Metathesis. Comparative Investigation of Two Different Catalyst Systems and Application to the Stereoselective Synthesis of Olfactory Lactones, Azamacrolides, and the Macrocyclic Perimeter of the Marine Alkaloid Nakadomarin A
Previously unknown ring closing metathesis reactions of diynes are described which open an efficient and stereoselective entry into macrocyclic (Z)-alkenes if the resulting cycloalkyne products are subjected to Lindlar reduction. This new two-step strategy offers significant advantages in stereochemical terms over conventional RCM of dienes which usually leads to (E,Z)-mixtures when applied to the formation of large rings. The tungsten alkylidyne complex (tBuO)3W⋮CCMe3(1a) and analogues thereof as well as a structurally unknown species formed in situ from Mo(CO)6 and p-chlorophenol effect the crucial alkyne metathesis reactions in a highly efficient manner, with the former catalyst being more tolerant toward structural variations of the substrates and polar functional groups. Applications to the stereoselective synthesis of the olfactory compounds ambrettolide 23 and yuzu lactone 24, the insect repellent azamacrolides epilachnene 31 and homoepilachnene 33, as well as to the fully functional building block 64 required for a total synthesis of the cytotoxic alkaloid nakadomarin A 51 highlight the relevance of this new concept for natural product chemistry. In the latter case, the diyne substrate 62 necessary for ring closing alkyne metathesis was obtained via a novel furan synthesis relying on a palladium-catalyzed opening of a vinyl epoxide followed by an oxidative cyclization of the heterocyclic ring
Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion
We apply the linear delta expansion to the quantum mechanical version of the
slow rollover transition which is an important feature of inflationary models
of the early universe. The method, which goes beyond the Gaussian
approximation, gives results which stay close to the exact solution for longer
than previous methods. It provides a promising basis for extension to a full
field theoretic treatment.Comment: 12 pages, including 4 figure
Onset of inflation in inhomogeneous cosmology
We study how the initial inhomogeneities of the universe affect the onset of
inflation in the closed universe. We consider the model of a chaotic inflation
which is driven by a massive scalar field. In order to construct an
inhomogeneous universe model, we use the long wavelength approximation ( the
gradient expansion method ). We show the condition of the inhomogeneities for
the universe to enter the inflationary phase.Comment: 22 pages including 12 eps figures, RevTe
Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials
We investigate the construction of diffusions consisting of infinitely
numerous Brownian particles moving in and interacting via
logarithmic functions (two-dimensional Coulomb potentials). These potentials
are very strong and act over a long range in nature. The associated equilibrium
states are no longer Gibbs measures. We present general results for the
construction of such diffusions and, as applications thereof, construct two
typical interacting Brownian motions with logarithmic interaction potentials,
namely the Dyson model in infinite dimensions and Ginibre interacting Brownian
motions. The former is a particle system in , while the latter is
in . Both models are translation and rotation invariant in space,
and as such, are prototypes of dimensions , respectively. The
equilibrium states of the former diffusion model are determinantal or Pfaffian
random point fields with sine kernels. They appear in the thermodynamical
limits of the spectrum of the ensembles of Gaussian random matrices such as
GOE, GUE and GSE. The equilibrium states of the latter diffusion model are the
thermodynamical limits of the spectrum of the ensemble of complex non-Hermitian
Gaussian random matrices known as the Ginibre ensemble.Comment: Published in at http://dx.doi.org/10.1214/11-AOP736 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Transplanckian inflation as gravity echoes
In this work, we show that, in the presence of non-minimal coupling to gravity, it is possible to generate sizeable tensor modes in single-field models without transplanckian field values. These transplanckian field values apparently needed in Einstein gravity to accommodate the experimental results may only be due to our insistence of imposing a minimal coupling of the inflaton field to gravity in a model with non-minimal couplings. We present three simple single-field models that prove that it is possible to accommodatea large tensor-to-scalar ratio without requiring transplanckian field values within the slow-roll regime
- …