14,050 research outputs found
Distributional Asymptotic Expansions of Spectral Functions and of the Associated Green Kernels
Asymptotic expansions of Green functions and spectral densities associated
with partial differential operators are widely applied in quantum field theory
and elsewhere. The mathematical properties of these expansions can be clarified
and more precisely determined by means of tools from distribution theory and
summability theory. (These are the same, insofar as recently the classic
Cesaro-Riesz theory of summability of series and integrals has been given a
distributional interpretation.) When applied to the spectral analysis of Green
functions (which are then to be expanded as series in a parameter, usually the
time), these methods show: (1) The "local" or "global" dependence of the
expansion coefficients on the background geometry, etc., is determined by the
regularity of the asymptotic expansion of the integrand at the origin (in
"frequency space"); this marks the difference between a heat kernel and a
Wightman two-point function, for instance. (2) The behavior of the integrand at
infinity determines whether the expansion of the Green function is genuinely
asymptotic in the literal, pointwise sense, or is merely valid in a
distributional (cesaro-averaged) sense; this is the difference between the heat
kernel and the Schrodinger kernel. (3) The high-frequency expansion of the
spectral density itself is local in a distributional sense (but not pointwise).
These observations make rigorous sense out of calculations in the physics
literature that are sometimes dismissed as merely formal.Comment: 34 pages, REVTeX; very minor correction
Recommended from our members
Tropidophis celiae
Number of pages: 8Geological SciencesIntegrative Biolog
Relativistic Many-Body Hamiltonian Approach to Mesons
We represent QCD at the hadronic scale by means of an effective Hamiltonian,
, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model,
chiral symmetry is explicity broken, however our approach is renormalizable and
also includes confinement through a linear potential with slope specified by
lattice gauge theory. This interaction generates an infrared integrable
singularity and we detail the computationally intensive procedure necessary for
numerical solution. We focus upon applications for the and quark
flavors and compute the mass spectrum for the pseudoscalar, scalar and vector
mesons. We also perform a comparative study of alternative many-body techniques
for approximately diagonalizing : BCS for the vacuum ground state; TDA and
RPA for the excited hadron states. The Dirac structure of the field theoretical
Hamiltonian naturally generates spin-dependent interactions, including tensor,
spin-orbit and hyperfine, and we clarify the degree of level splitting due to
both spin and chiral symmetry effects. Significantly, we find that roughly
two-thirds of the - mass difference is due to chiral symmetry and
that only the RPA preserves chiral symmetry. We also document how hadronic mass
scales are generated by chiral symmetry breaking in the model vacuum. In
addition to the vacuum condensates, we compute meson decay constants and detail
the Nambu-Goldstone realization of chiral symmetry by numerically verifying the
Gell-Mann-Oaks-Renner relation. Finally, by including D waves in our charmonium
calculation we have resolved the anomalous overpopulation of states
relative to observation
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
Dynamical Mass Generation in Landau gauge QCD
We summarise results on the infrared behaviour of Landau gauge QCD from the
Green's functions approach and lattice calculations. Approximate,
nonperturbative solutions for the ghost, gluon and quark propagators as well as
first results for the quark-gluon vertex from a coupled set of Dyson-Schwinger
equations are compared to quenched and unquenched lattice results. Almost
quantitative agreement is found for all three propagators. Similar effects of
unquenching are found in both approaches. The dynamically generated quark
masses are close to `phenomenological' values. First results for the
quark-gluon vertex indicate a complex tensor structure of the non-perturbative
quark-gluon interaction.Comment: 6 pages, 6 figures, Summary of a talk given at the international
conference QCD DOWN UNDER, March 10 - 19, Adelaide, Australi
GTI-space : the space of generalized topological indices
A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given
Locally projective monoidal model structure for complexes of quasi-coherent sheaves on P^1(k)
We will generalize the projective model structure in the category of
unbounded complexes of modules over a commutative ring to the category of
unbounded complexes of quasi-coherent sheaves over the projective line.
Concretely we will define a locally projective model structure in the category
of complexes of quasi-coherent sheaves on the projective line. In this model
structure the cofibrant objects are the dg-locally projective complexes. We
also describe the fibrations of this model structure and show that the model
structure is monoidal. We point out that this model structure is necessarily
different from other known model structures such as the injective model
structure and the locally free model structure
- …