122,092 research outputs found
Total Cofibres of Diagrams of Spectra
If Y is a diagram of spectra indexed by an arbitrary poset C together with a
specified sub-poset D, we define the total cofibre \Gamma (Y) of Y as the
strict cofibre of the map from hocolim_D (Y) to hocolim_C (Y). We construct a
comparison map from the homotopy limit of Y to a looping of a fibrant
replacement of Gamma (Y), and characterise those poset pairs (C,D) for which
this comparison map is a stable equivalence. The characterisation is given in
terms of stable cohomotopy of spaces related to C and D. For example, if C is a
finite polytopal complex with underlying space an m-ball with boundary sphere
D, then holim_C (Y) and \Gamma(Y) agree up to m-fold looping and up to stable
equivalence. As an application of the general result we give a spectral
sequence for the homotopy groups of \Gamma(Y) with E_2-term involving higher
derived inverse limits of \pi_* (Y), generalising earlier constructions for
space-valued diagrams indexed by the face lattice of a polytope.Comment: 11 pages; LaTeX source code uses Paul Taylor's "diagrams" and "QED"
macro packages; some diagrams may not display correctly with DVI viewers;
paper also available at http://nyjm.albany.edu:8000/j/2005/11-16.htm
Exponentiation for products of Wilson lines within the generating function approach
We present the generating function approach to the perturbative
exponentiation of correlators of a product of Wilson lines and loops. The
exponentiated expression is presented in closed form as an algebraic function
of correlators of known operators, which can be seen as a generating function
for web diagrams. The expression is naturally split onto two parts: the
exponentiation kernel, which accumulates all non-trivial information about web
diagrams, and the defect of exponentiation, which reconstructs the matrix
exponent and is a function of the exponentiation kernel. The detailed
comparison of the presented approach with existing approaches to exponentiation
is presented as well. We also give examples of calculations within the
generating function exponentiation, namely, we consider different
configurations of light-like Wilson lines in the multi-gluon-exchange-webs
(MGEW) approximation. Within this approximation the corresponding correlators
can be calculated exactly at any order of perturbative expansion by only
algebraic manipulations. The MGEW approximation shows violation of the dipole
formula for infrared singularities at three-loop order.Comment: 33 pages, 5 figures; updated to match journal versio
Wick's theorem for q-deformed boson operators
In this paper combinatorial aspects of normal ordering arbitrary words in the
creation and annihilation operators of the q-deformed boson are discussed. In
particular, it is shown how by introducing appropriate q-weights for the
associated ``Feynman diagrams'' the normally ordered form of a general
expression in the creation and annihilation operators can be written as a sum
over all q-weighted Feynman diagrams, representing Wick's theorem in the
present context.Comment: 9 page
The LPM effect in sequential bremsstrahlung
The splitting processes of bremsstrahlung and pair production in a medium are
coherent over large distances in the very high energy limit, which leads to a
suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We analyze the
case when the coherence lengths of two consecutive splitting processes overlap,
which is important for understanding corrections to standard treatments of the
LPM effect in QCD. Previous authors have analyzed this problem in the case of
overlapping double bremsstrahlung where at least one of the bremsstrahlung
gluons is soft. Here we show how to generalize to include the case where both
splittings are hard. A number of techniques must be developed, and so in this
paper we simplify by (i) restricting attention to a subset of the interference
effects, which we call the "crossed" diagrams, and (ii) working in the
large- limit. We first develop some general formulas that could in
principle be implemented numerically (with substantial difficulty). To make
more analytic progress, we then focus on the case of a thick, homogeneous
medium and make the multiple scattering approximation (also known as the or harmonic approximation) appropriate at high energy. We show that the
differential rate for overlapping double bremsstrahlung of
gluons with momentum fractions and can then be reduced to the
calculation of a 1-dimensional integral, which we perform numerically. [Though
this paper is unfortunately long, our introduction is enough for getting the
gist of the method.]Comment: 85 pages, 30 figures [only change from v5: fixed trivial typo of a
missing bar in eq. (2.20a). The authors are obsessive.
On the anomalous dimension for the transversity distribution
We show that a standard calculation of the splitting function for the
nonsinglet structure function h_1 does not lead to the expected result. The
calculation is compared to the corresponding derivation of the splitting
function for the nonsinglet polarized structure function g_1. We analyze
possible explanations for the unexpected result and discuss its implications.
PACS: 11.10.Hi; 11.40.-q; 11.55.Ds; 13.88.+eComment: 8 pages, 1 figure, 2 references adde
- …