7 research outputs found
Variational Approach to Real-Time Evolution of Yang-Mills Gauge Fields on a Lattice
Applying a variational method to a Gaussian wave ansatz, we have derived a
set of semi-classical evolution equations for SU(2) lattice gauge fields, which
take the classical form in the limit of a vanishing width of the Gaussian wave
packet. These equations are used to study the quantum effects on the classical
evolutions of the lattice gauge fields.Comment: LaTeX, 12 pages, 5 figures contained in a separate uuencoded file,
DUKE-TH-93-4
A Matrix Approach to Numerical Solution of the DGLAP Evolution Equations
A matrix-based approach to numerical integration of the DGLAP evolution
equations is presented. The method arises naturally on discretisation of the
Bjorken x variable, a necessary procedure for numerical integration. Owing to
peculiar properties of the matrices involved, the resulting equations take on a
particularly simple form and may be solved in closed analytical form in the
variable t=ln(alpha_0/alpha). Such an approach affords parametrisation via data
x bins, rather than fixed functional forms. Thus, with the aid of the full
correlation matrix, appraisal of the behaviour in different x regions is
rendered more transparent and free of pollution from unphysical
cross-correlations inherent to functional parametrisations. Computationally,
the entire programme results in greater speed and stability; the matrix
representation developed is extremely compact. Moreover, since the parameter
dependence is linear, fitting is very stable and may be performed analytically
in a single pass over the data values.Comment: 13 pages, no figures, typeset with revtex4 and uses packages:
acromake, amssym
The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions
According to a rederivation - due to Collins and Qiu - the DGLAP equation can
be reinterpreted (in leading order) in a probabilistic way. This form of the
equation has been used indirectly to prove the bound
between polarized and unpolarized distributions, or positivity of the helicity
distributions, for any . We reanalize this issue by performing a detailed
numerical study of the positivity bounds of the helicity distributions. To
obtain the numerical solution we implement an x-space based algorithm for
polarized and unpolarized distributions to next-to-leading order in ,
which we illustrate. We also elaborate on some of the formal properties of the
Collins-Qiu form and comment on the underlying regularization, introduce a
Kramers-Moyal expansion of the equation and briefly analize its Fokker-Planck
approximation. These follow quite naturally once the master version is given.
We illustrate this expansion both for the valence quark distribution and
for the transverse spin distribution .Comment: 38 pages, 27 figures, Dedicated to Prof. Pierre Ramond for his 60th
birthda
The Free Energy Of Hot Gauge Theories
The total perturbative contribution to the free-energy of hot SU(3) gauge
theory is argued to lie significantly higher than the full result obtained by
lattice simulations. This then suggests the existence of large non-perturbative
corrections even at temperatures a few times above the critical temperature.
Some speculations are then made on the nature and origin of the
non-perturbative corrections. The analysis is then carried out for quantum
chromodynamics, gauge theories, and quantum electrodynamics, leading
to a conjecture and one more speculation.Comment: Revised Journal version;25 pages Latex and 11 .eps figures in
separate file. Requires epsf.st
Perturbative QCD Analysis of Meson Decays
Resummation of large QCD radiative corrections, including leading and
next-to-leading logarithms, in pion electromagnetic form factor is reviewed.
Similar formalism is applied to exclusive processes involving heavy mesons, and
leads to Sudakov suppression for the semi-leptonic decay . It is
found that, with the inclusion of Sudakov effects, perturbative QCD analysis of
this decay is possible for the energy fraction of the pion above 0.3. By
combining predictions from the soft pion theorems, we estimate that the upper
limit of the KM matrix element is roughly 0.003.Comment: 26 pages in latex, figures are available for reques