882 research outputs found

### Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory
using a (new) Delta -regulator. To be well-defined, the effective theory
requires zero-bin subtractions for the collinear sectors. The zero-bin
subtractions depend on the gauge boson mass M and are not scaleless. They have
both finite and 1/epsilon contributions, and are needed to give the correct
anomalous dimension and low-scale matching contributions. We also demonstrate
the necessity of zero-bin subtractions for soft-collinear factorization. We
find that after zero-bin subtractions the form factor is the sum of the
collinear contributions 'minus' a soft mass-mode contribution, in agreement
with a previous result of Idilbi and Mehen in QCD. This appears to conflict
with the method-of-regions approach, where one gets the sum of contributions
from different regions.Comment: 9 pages, 5 figures. V2:ref adde

### The quantum Casimir operators of \Uq and their eigenvalues

We show that the quantum Casimir operators of the quantum linear group
constructed in early work of Bracken, Gould and Zhang together with one extra
central element generate the entire center of \Uq. As a by product of the
proof, we obtain intriguing new formulae for eigenvalues of these quantum
Casimir operators, which are expressed in terms of the characters of a class of
finite dimensional irreducible representations of the classical general linear
algebra.Comment: 10 page

### The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange

The resummation of soft gluon exchange for QCD hard scattering requires a
matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2
to n massless processes for the first time at two loops. Using color generator
notation, we show that it is proportional to the one-loop matrix. This result
reproduces all pole terms in dimensional regularization of the explicit
calculations of massless 2 to 2 amplitudes in the literature, and it predicts
all poles at next-to-next-to-leading order in any 2 to n process that has been
computed at next-to-leading order. The proportionality of the one- and two-loop
matrices makes possible the resummation in closed form of the
next-to-next-to-leading logarithms and poles in dimensional regularization for
the 2 to n processes.Comment: 5 pages, 1 figure, revte

### A new proof of the Bianchi type IX attractor theorem

We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state. The
`Bianchi type IX attractor theorem' states that the past asymptotic behavior of
generic type IX solutions is governed by Bianchi type I and II vacuum states
(Mixmaster attractor). We give a comparatively short and self-contained new
proof of this theorem. The proof we give is interesting in itself, but more
importantly it illustrates and emphasizes that type IX is special, and to some
extent misleading when one considers the broader context of generic models
without symmetries.Comment: 26 pages, 5 figure

### Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard
Boyer-Lindquist coordinates to its corresponding form adapted to the natural
local coordinates of an observer at rest at a fixed position in the equatorial
plane, i.e., Fermi coordinates for the neighborhood of a static observer world
line, is derived and discussed in a way which extends to any uniformly
circularly orbiting observer there.Comment: 15 page latex iopart class documen

### Electrocardiogram of the Mixmaster Universe

The Mixmaster dynamics is revisited in a new light as revealing a series of
transitions in the complex scale invariant scalar invariant of the Weyl
curvature tensor best represented by the speciality index $\mathcal{S}$, which
gives a 4-dimensional measure of the evolution of the spacetime independent of
all the 3-dimensional gauge-dependent variables except for the time used to
parametrize it. Its graph versus time characterized by correlated isolated
pulses in its real and imaginary parts corresponding to curvature wall
collisions serves as a sort of electrocardiogram of the Mixmaster universe,
with each such pulse pair arising from a single circuit or ``complex pulse''
around the origin in the complex plane. These pulses in the speciality index
and their limiting points on the real axis seem to invariantly characterize
some of the so called spike solutions in inhomogeneous cosmology and should
play an important role as a gauge invariant lens through which to view current
investigations of inhomogeneous Mixmaster dynamics.Comment: version 3: 20 pages iopart style, 19 eps figure files for 8 latex
figures; added example of a transient true spike to contrast with the
permanent true spike example from the Lim family of true spike solutions;
remarks in introduction and conclusion adjusted and toned down; minor
adjustments to the remaining tex

### Monotonic functions in Bianchi models: Why they exist and how to find them

All rigorous and detailed dynamical results in Bianchi cosmology rest upon
the existence of a hierarchical structure of conserved quantities and monotonic
functions. In this paper we uncover the underlying general mechanism and derive
this hierarchical structure from the scale-automorphism group for an
illustrative example, vacuum and diagonal class A perfect fluid models. First,
kinematically, the scale-automorphism group leads to a reduced dynamical system
that consists of a hierarchy of scale-automorphism invariant sets. Second, we
show that, dynamically, the scale-automorphism group results in
scale-automorphism invariant monotone functions and conserved quantities that
restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio

### The Kazhdan-Lusztig conjecture for W-algebras

The main result in this paper is the character formula for arbitrary
irreducible highest weight modules of W algebras. The key ingredient is the
functor provided by quantum Hamiltonian reduction, that constructs the W
algebras from affine Kac-Moody algebras and in a similar fashion W modules from
KM modules. Assuming certain properties of this functor, the W characters are
subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The
result can be formulated in terms of a double coset of the Weyl group of the KM
algebra: the Hasse diagrams give the embedding diagrams of the Verma modules
and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.Comment: uuencoded file, 29 pages latex, 5 figure

### Quantum state transfer in a q-deformed chain

We investigate the quantum state transfer in a chain of particles satisfying
q-deformed oscillators algebra. This general algebraic setting includes the
spin chain and the bosonic chain as limiting cases. We study conditions for
perfect state transfer depending on the number of sites and excitations on the
chain. They are formulated by means of irreducible representations of a quantum
algebra realized through Jordan-Schwinger maps. Playing with deformation
parameters, we can study the effects of nonlinear perturbations or interpolate
between the spin and bosonic chain.Comment: 13 pages, 4 figure

### Circular holonomy in the Taub-NUT spacetime

Parallel transport around closed circular orbits in the equatorial plane of
the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic
monopole parameter on circular holonomy transformations. Investigating the
boost/rotation decomposition of the connection 1-form matrix evaluated along
these orbits, one finds a situation that reflects the behavior of the general
orthogonally transitive stationary axisymmetric case and indeed along Killing
trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure

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