142 research outputs found
Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory
A class of singular integral operators, encompassing two physically relevant
cases arising in perturbative QCD and in classical fluid dynamics, is presented
and analyzed. It is shown that three special values of the parameters allow for
an exact eigenfunction expansion; these can be associated to Riemannian
symmetric spaces of rank one with positive, negative or vanishing curvature.
For all other cases an accurate semiclassical approximation is derived, based
on the identification of the operators with a peculiar Schroedinger-like
operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11
The trace of the heat kernel on a compact hyperbolic 3-orbifold
The heat coefficients related to the Laplace-Beltrami operator defined on the
hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the
discrete group \Ga contains elliptic and hyperbolic elements. It is shown
that while hyperbolic elements give only exponentially vanishing corrections to
the trace of the heat kernel, elliptic elements modify all coefficients of the
asymptotic expansion, but the Weyl term, which remains unchanged. Some physical
consequences are briefly discussed in the examples.Comment: 11 page
Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type
We obtain a general expression for a Wigner transform (Wigner function) on
symmetric spaces of non-compact type and study the Weyl calculus of
pseudodifferential operators on them
A Hierarchical Array of Integrable Models
Motivated by Harish-Chandra theory, we construct, starting from a simple
CDD\--pole \--matrix, a hierarchy of new \--matrices involving ever
``higher'' (in the sense of Barnes) gamma functions.These new \--matrices
correspond to scattering of excitations in ever more complex integrable
models.From each of these models, new ones are obtained either by
``\--deformation'', or by considering the Selberg-type Euler products of
which they represent the ``infinite place''. A hierarchic array of integrable
models is thus obtained. A remarkable diagonal link in this array is
established.Though many entries in this array correspond to familiar integrable
models, the array also leads to new models. In setting up this array we were
led to new results on the \--gamma function and on the \--deformed
Bloch\--Wigner function.Comment: 18 pages, EFI-92-2
Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
In this article we apply the methods outlined in the previous paper of this
series to the particular set of states obtained by choosing the complexifier to
be a Laplace operator for each edge of a graph. The corresponding coherent
state transform was introduced by Hall for one edge and generalized by
Ashtekar, Lewandowski, Marolf, Mour\~ao and Thiemann to arbitrary, finite,
piecewise analytic graphs. However, both of these works were incomplete with
respect to the following two issues : (a) The focus was on the unitarity of the
transform and left the properties of the corresponding coherent states
themselves untouched. (b) While these states depend in some sense on
complexified connections, it remained unclear what the complexification was in
terms of the coordinates of the underlying real phase space. In this paper we
resolve these issues, in particular, we prove that this family of states
satisfies all the usual properties : i) Peakedness in the configuration,
momentum and phase space (or Bargmann-Segal) representation, ii) Saturation of
the unquenched Heisenberg uncertainty bound. iii) (Over)completeness. These
states therefore comprise a candidate family for the semi-classical analysis of
canonical quantum gravity and quantum gauge theory coupled to quantum gravity,
enable error-controlled approximations and set a new starting point for {\it
numerical canonical quantum general relativity and gauge theory}. The text is
supplemented by an appendix which contains extensive graphics in order to give
a feeling for the so far unknown peakedness properties of the states
constructed.Comment: 70 pages, LATEX, 29 figure
Gauge Field Theory Coherent States (GCS) : I. General Properties
In this article we outline a rather general construction of diffeomorphism
covariant coherent states for quantum gauge theories.
By this we mean states , labelled by a point (A,E) in the
classical phase space, consisting of canonically conjugate pairs of connections
A and electric fields E respectively, such that (a) they are eigenstates of a
corresponding annihilation operator which is a generalization of A-iE smeared
in a suitable way, (b) normal ordered polynomials of generalized annihilation
and creation operators have the correct expectation value, (c) they saturate
the Heisenberg uncertainty bound for the fluctuations of and
(d) they do not use any background structure for their definition, that is,
they are diffeomorphism covariant.
This is the first paper in a series of articles entitled ``Gauge Field Theory
Coherent States (GCS)'' which aim at connecting non-perturbative quantum
general relativity with the low energy physics of the standard model. In
particular, coherent states enable us for the first time to take into account
quantum metrics which are excited {\it everywhere} in an asymptotically flat
spacetime manifold. The formalism introduced in this paper is immediately
applicable also to lattice gauge theory in the presence of a (Minkowski)
background structure on a possibly {\it infinite lattice}.Comment: 40 pages, LATEX, no figure
Counting and effective rigidity in algebra and geometry
The purpose of this article is to produce effective versions of some rigidity
results in algebra and geometry. On the geometric side, we focus on the
spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic
hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum
determines the commensurability class of the 2-manifold (resp., 3-manifold). We
establish effective versions of these rigidity results by ensuring that, for
two incommensurable arithmetic manifolds of bounded volume, the length sets
(resp., the complex length sets) must disagree for a length that can be
explicitly bounded as a function of volume. We also prove an effective version
of a similar rigidity result established by the second author with Reid on a
surface analog of the length spectrum for hyperbolic 3-manifolds. These
effective results have corresponding algebraic analogs involving maximal
subfields and quaternion subalgebras of quaternion algebras. To prove these
effective rigidity results, we establish results on the asymptotic behavior of
certain algebraic and geometric counting functions which are of independent
interest.Comment: v.2, 39 pages. To appear in Invent. Mat
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space-like separation between the proton and electron in
the hydrogen atom. According to the Copenhagen school of quantum mechanics, the
proton is sitting in the absolute Lorentz frame. If this hydrogen atom is
observed from a different Lorentz frame, there is a time-like separation
linearly mixed with the Bohr radius. Indeed, the time-separation is one of the
essential variables in high-energy hadronic physics where the hadron is a bound
state of the quarks, while thoroughly hidden in the present form of quantum
mechanics. It will be concluded that this variable is hidden in Feynman's rest
of the universe. It is noted first that Feynman's Lorentz-invariant
differential equation for the bound-state quarks has a set of solutions which
describe all essential features of hadronic physics. These solutions explicitly
depend on the time separation between the quarks. This set also forms the
mathematical basis for two-mode squeezed states in quantum optics, where both
photons are observable, but one of them can be treated a variable hidden in the
rest of the universe. The physics of this two-mode state can then be translated
into the time-separation variable in the quark model. As in the case of the
un-observed photon, the hidden time-separation variable manifests itself as an
increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the
Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be
published in one of the AIP Conference Proceedings serie
Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces
We find necessary and sufficient conditions for a finite K–bi–invariant
measure on a compact Gelfand pair (G, K) to have a square–integrable
density. For convolution semigroups, this is equivalent to having a
continuous density in positive time. When (G, K) is a compact Riemannian
symmetric pair, we study the induced transition density for
G–invariant Feller processes on the symmetric space X = G/K. These
are obtained as projections of K–bi–invariant L´evy processes on G,
whose laws form a convolution semigroup. We obtain a Fourier series
expansion for the density, in terms of spherical functions, where the
spectrum is described by Gangolli’s L´evy–Khintchine formula. The
density of returns to any given point on X is given by the trace of
the transition semigroup, and for subordinated Brownian motion, we
can calculate the short time asymptotics of this quantity using recent
work of Ba˜nuelos and Baudoin. In the case of the sphere, there is an
interesting connection with the Funk–Hecke theorem
Maternal characteristics associated with the dietary intake of nitrates, nitrites, and nitrosamines in women of child-bearing age: a cross-sectional study
<p>Abstract</p> <p>Background</p> <p>Multiple <it>N</it>-nitroso compounds have been observed in animal studies to be both mutagenic and teratogenic. Human exposure to <it>N</it>-nitroso compounds and their precursors, nitrates and nitrites, can occur through exogenous sources, such as diet, drinking water, occupation, or environmental exposures, and through endogenous exposures resulting from the formation of <it>N</it>-nitroso compounds in the body. Very little information is available on intake of nitrates, nitrites, and nitrosamines and factors related to increased consumption of these compounds.</p> <p>Methods</p> <p>Using survey and dietary intake information from control women (with deliveries of live births without major congenital malformations during 1997-2004) who participated in the National Birth Defects Prevention Study (NBDPS), we examined the relation between various maternal characteristics and intake of nitrates, nitrites, and nitrosamines from dietary sources. Estimated intake of these compounds was obtained from the Willet Food Frequency Questionnaire as adapted for the NBDPS. Multinomial logistic regression models were used to estimate odds ratios and 95% confidence intervals for the consumption of these compounds by self-reported race/ethnicity and other maternal characteristics.</p> <p>Results</p> <p>Median intake per day for nitrates, nitrites, total nitrites (nitrites + 5% nitrates), and nitrosamines was estimated at 40.48 mg, 1.53 mg, 3.69 mg, and 0.472 μg respectively. With the lowest quartile of intake as the referent category and controlling for daily caloric intake, factors predicting intake of these compounds included maternal race/ethnicity, education, body mass index, household income, area of residence, folate intake, and percent of daily calories from dietary fat. Non-Hispanic White participants were less likely to consume nitrates, nitrites, and total nitrites per day, but more likely to consume dietary nitrosamines than other participants that participated in the NBDPS. Primary food sources of these compounds also varied by maternal race/ethnicity.</p> <p>Conclusions</p> <p>Results of this study indicate that intake of nitrates, nitrites, and nitrosamines vary considerably by race/ethnicity, education, body mass index, and other characteristics. Further research is needed regarding how consumption of foods high in nitrosamines and <it>N</it>-nitroso precursors might relate to risk of adverse pregnancy outcomes and chronic diseases.</p
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