3,118 research outputs found
Cosmography, Decelerating Past, and Cosmological Models: Learning the Bayesian Way
In this paper, using a significantly improved version of the
model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ,
614, 1), we address an important question: Was there a decelerating past for
the universe? To answer this, the Bayes's probability theory is employed, which
is the most appropriate tool for quantifying our knowledge when it changes
through the acquisition of new data. The cosmographic approach helps to sort
out the models in which the universe was always accelerating from those in
which it decelerated for at least some time in the period of interest. Bayesian
model comparison technique is used to discriminate these rival hypotheses with
the aid of recent releases of supernova data. We also attempt to provide and
improve another example of Bayesian model comparison, performed between some
Friedmann models, using the same data. Our conclusion, which is consistent with
other approaches, is that the apparent magnitude-redshift data alone cannot
discriminate these competing hypotheses. We also argue that the lessons learnt
using Bayesian theory are extremely valuable to avoid frequent U-turns in
cosmology.Comment: Accepted for publication in The Astrophysical Journal (ApJ
Black Holes Surrounded by Uniformly Rotating Rings
Highly accurate numerical solutions to the problem of Black Holes surrounded
by uniformly rotating rings in axially symmetric, stationary spacetimes are
presented. The numerical methods developed to handle the problem are discussed
in some detail. Related Newtonian problems are described and numerical results
provided, which show that configurations can reach an inner mass-shedding limit
as the mass of the central object increases. Exemplary results for the full
relativistic problem for rings of constant density are given and the
deformation of the event horizon due to the presence of the ring is
demonstrated. Finally, we provide an example of a system for which the angular
momentum of the central Black Hole divided by the square of its mass exceeds
one.Comment: 12 pages, 14 figures, revtex, v4: minor changes, Eq. (17) corrected,
corresponds to version in PR
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
Two-channel Kondo model as a generalized one-dimensional inverse square long-range Haldane-Shastry spin model
Majorana fermion representations of the algebra associated with spin, charge,
and flavor currents have been used to transform the two-channel Kondo
Hamiltonian. Using a path integral formulation, we derive a reduced effective
action with long-range impurity spin-spin interactions at different imaginary
times. In the semiclassical limit, it is equivalent to a one-dimensional
Heisenberg spin chain with two-spin, three-spin, etc. long-range interactions,
as a generalization of the inverse-square long-range Haldane-Shastry spin
model. In this representation the elementary excitations are "semions", and the
non-Fermi-liquid low-energy properties of the two-channel Kondo model are
recovered.Comment: 4 pages, no figure, to be published in J. Phys.: Condens. Matter,
200
An analyst's take on the BPHZ theorem
We provide a self-contained formulation of the BPHZ theorem in the Euclidean
context, which yields a systematic procedure to "renormalise" otherwise
divergent integrals appearing in generalised convolutions of functions with a
singularity of prescribed order at their origin. We hope that the formulation
given in this article will appeal to an analytically minded audience and that
it will help to clarify to what extent such renormalisations are arbitrary (or
not). In particular, we do not assume any background whatsoever in quantum
field theory and we stay away from any discussion of the physical context in
which such problems typically arise.Comment: Accepted versio
The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure
Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
Hamiltonian light-front field theory can be used to solve for hadron states
in QCD. To this end, a method has been developed for systematic renormalization
of Hamiltonian light-front field theories, with the hope of applying the method
to QCD. It assumed massless particles, so its immediate application to QCD is
limited to gluon states or states where quark masses can be neglected. This
paper builds on the previous work by including particle masses
non-perturbatively, which is necessary for a full treatment of QCD. We show
that several subtle new issues are encountered when including masses
non-perturbatively. The method with masses is algebraically and conceptually
more difficult; however, we focus on how the methods differ. We demonstrate the
method using massive phi^3 theory in 5+1 dimensions, which has important
similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra
disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final
published versio
Relativistic Dyson Rings and Their Black Hole Limit
In this Letter we investigate uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding
field equations are solved by means of a multi-domain spectral method, which
yields highly accurate numerical solutions. For a prescribed, sufficiently
large ratio of inner to outer coordinate radius, the toroids exhibit a
continuous transition to the extreme Kerr black hole. Otherwise, the most
relativistic configuration rotates at the mass-shedding limit. For a given
mass-density, there seems to be no bound to the gravitational mass as one
approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references
added, accepted for publication in Astrophys. J. Let
On the Isomorphic Description of Chiral Symmetry Breaking by Non-Unitary Lie Groups
It is well-known that chiral symmetry breaking (SB) in QCD with
light quark flavours can be described by orthogonal groups as , due to local isomorphisms. Here we discuss the question how specific
this property is. We consider generalised forms of SB involving an
arbitrary number of light flavours of continuum or lattice fermions, in various
representations. We search systematically for isomorphic descriptions by
non-unitary, compact Lie groups. It turns out that there are a few alternative
options in terms of orthogonal groups, while we did not find any description
entirely based on symplectic or exceptional Lie groups. If we adapt such an
alternative as the symmetry breaking pattern for a generalised Higgs mechanism,
we may consider a Higgs particle composed of bound fermions and trace back the
mass generation to SB. In fact, some of the patterns that we encounter
appear in technicolour models. In particular if one observes a Higgs mechanism
that can be expressed in terms of orthogonal groups, we specify in which cases
it could also represent some kind of SB of techniquarks.Comment: 18 pages, to appear in Int. J. Mod. Phys.
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