21,737 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
Direct measurement of penetration length in ultra-thin and/or mesoscopic superconducting structures
We describe a method for direct measurement of the magnetic penetration
length in thin (10 - 100 nm) superconducting structures having overall
dimensions in the range 1 to 100 micrometers. The method is applicable for
broadband magnetic fields from dc to MHz frequencies.Comment: Accepted by Journal of Applied P:hysics (Jun 2006).5 pages, 5 figure
Finite Symmetry of Leptonic Mass Matrices
We search for possible symmetries present in the leptonic mixing data from
SU(3) subgroups of order up to 511. Theoretical results based on symmetry are
compared with global fits of experimental data in a chi-squared analysis,
yielding the following results. There is no longer a group that can produce all
the mixing data without a free parameter, but a number of them can accommodate
the first or the second column of the mixing matrix. The only group that fits
the third column is . It predicts and
, in good agreement with experimental results.Comment: Version to appear in Physical Review
Implementing Unitarity in Perturbation Theory
Unitarity cannot be perserved order by order in ordinary perturbation theory
because the constraint UU^\dagger=\1 is nonlinear. However, the corresponding
constraint for , being , is linear so it can be
maintained in every order in a perturbative expansion of . The perturbative
expansion of may be considered as a non-abelian generalization of the
linked-cluster expansion in probability theory and in statistical mechanics,
and possesses similar advantages resulting from separating the short-range
correlations from long-range effects. This point is illustrated in two QCD
examples, in which delicate cancellations encountered in summing Feynman
diagrams of are avoided when they are calculated via the perturbative expansion
of . Applications to other problems are briefly discussed.Comment: to appear in Phys. Rev.
H ∞ and positive-real control for linear neutral delay systems
This note is concerned with the H ∞and positive-real control problems for linear neutral delay systems. The purpose of H ∞control is the design of a memoryless state feedback controller which stabilizes the neutral delay system and reduces the H ∞norm of the closed-loop transfer function from the disturbance to the controlled output to a prescribed level, while the purpose of positive-real control is to design a memoryless state feedback controller such that the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of the desired controllers are given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expected memoryless state feedback controllers can be easily constructed via convex optimization.published_or_final_versio
Small-Recoil Approximation
In this review we discuss a technique to compute and to sum a class of
Feynman diagrams, and some of its applications. These are diagrams containing
one or more energetic particles that suffer very little recoil in their
interactions. When recoil is completely neglected, a decomposition formula can
be proven. This formula is a generalization of the well-known eikonal formula,
to non-abelian interactions. It expresses the amplitude as a sum of products of
irreducible amplitudes, with each irreducible amplitude being the amplitude to
emit one, or several mutually interacting, quasi-particles. For abelian
interaction a quasi-particle is nothing but the original boson, so this
decomposition formula reduces to the eikonal formula. In non-abelian situations
each quasi-particle can be made up of many bosons, though always with a total
quantum number identical to that of a single boson. This decomposition enables
certain amplitudes of all orders to be summed up into an exponential form, and
it allows subleading contributions of a certain kind, which is difficult to
reach in the usual way, to be computed. For bosonic emissions from a heavy
source with many constituents, a quasi-particle amplitude turns out to be an
amplitude in which all bosons are emitted from the same constituent. For
high-energy parton-parton scattering in the near-forward direction, the
quasi-particle turns out to be the Reggeon, and this formalism shows clearly
why gluons reggeize but photons do not. The ablility to compute subleading
terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to
asymptotic energies, in a unitary way preserving the Froissart bound. We also
consider recoil corrections for abelian interactions in order to accommodate
the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure
Multiple Reggeon Exchange from Summing QCD Feynman Diagrams
Multiple reggeon exchange supplies subleading logs that may be used to
restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that
the sum of Feynman diagrams to all orders gives rise to such multiple regge
exchanges. This question cannot be easily tackled in the usual way except for
very low-order diagrams, on account of delicate cancellations present in the
sum which necessitate individual Feynman diagrams to be computed to subleading
orders. Moreover, it is not clear that sums of high-order Feynman diagrams with
complicated criss-crossing of lines can lead to factorization implied by the
multi-regge scenario. Both of these difficulties can be overcome by using the
recently developed nonabelian cut diagrams. We are then able to show that the
sum of -channel-ladder diagrams to all orders does lead to such multiple
reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages
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