4,969,084 research outputs found
Generalized Background-Field Method
The graphical method discussed previously can be used to create new gauges
not reachable by the path-integral formalism. By this means a new gauge is
designed for more efficient two-loop QCD calculations. It is related to but
simpler than the ordinary background-field gauge, in that even the triple-gluon
vertices for internal lines contain only four terms, not the usual six. This
reduction simplifies the calculation inspite of the necessity to include other
vertices for compensation. Like the ordinary background-field gauge, this
generalized background-field gauge also preserves gauge invariance of the
external particles. As a check of the result and an illustration for the
reduction in labour, an explicit calculation of the two-loop QCD
-function is carried out in this new gauge. It results in a saving of
45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip
Test-field method for mean-field coefficients with MHD background
Aims: The test-field method for computing turbulent transport coefficients
from simulations of hydromagnetic flows is extended to the regime with a
magnetohydrodynamic (MHD) background. Methods: A generalized set of test
equations is derived using both the induction equation and a modified momentum
equation. By employing an additional set of auxiliary equations, we derive
linear equations describing the response of the system to a set of prescribed
test fields. Purely magnetic and MHD backgrounds are emulated by applying an
electromotive force in the induction equation analogously to the ponderomotive
force in the momentum equation. Both forces are chosen to have Roberts
flow-like geometry. Results: Examples with an MHD background are studied where
the previously used quasi-kinematic test-field method breaks down. In cases
with homogeneous mean fields it is shown that the generalized test-field method
produces the same results as the imposed-field method, where the field-aligned
component of the actual electromotive force from the simulation is used.
Furthermore, results for the turbulent diffusivity tensor are given, which are
inaccessible to the imposed-field method. For MHD backgrounds, new mean-field
effects are found that depend on the occurrence of cross-correlations between
magnetic and velocity fluctuations. For strong imposed fields, is
found to be quenched proportional to the fourth power of the field strength,
regardless of the type of background studied.Comment: 17 pages, 10 figures, submitted to Astronomy & Astrophysic
Baryons in the Field Correlator Method
The ground and -wave excited states of , and baryons are
studied in the framework of the field correlator method using the running
strong coupling constant in the Coulomb-like part of the three-quark potential.
The string correction for the confinement potential of the orbitally excited
baryons, which is the leading contribution of the proper inertia of the
rotating strings, is estimated.Comment: 6 pages, 2 figures. Talk given at APS April Meeting, Denver,
Colorado, May 2-5, 2009 and at the Tenth Conference on the Intersections of
Particle and Nuclear Physics (CIPANP 2009), San Diego, California, May 26-31,
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Duality relations in the auxiliary field method
The eigenenergies of a system of
identical particles with a mass are functions of the various radial quantum
numbers and orbital quantum numbers . Approximations
of these eigenenergies, depending on a principal quantum number
, can be obtained in the framework of the auxiliary field
method. We demonstrate the existence of numerous exact duality relations
linking quantities and for various forms of the
potentials (independent of and ) and for both nonrelativistic and
semirelativistic kinematics. As the approximations computed with the auxiliary
field method can be very close to the exact results, we show with several
examples that these duality relations still hold, with sometimes a good
accuracy, for the exact eigenenergies
Semirelativistic Hamiltonians and the auxiliary field method
Approximate analytical closed energy formulas for semirelativistic
Hamiltonians of the form are obtained within
the framework of the auxiliary field method. This method, which is equivalent
to the envelope theory, has been recently proposed as a powerful tool to get
approximate analytical solutions of the Schr\"odinger equation. Various shapes
for the potential are investigated: power-law, funnel, square root, and
Yukawa. A comparison with the exact results is discussed in detail
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