933 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
Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model
To analyze linear field equations on a locally homogeneous spacetime by means
of separation of variables, it is necessary to set up appropriate harmonics
according to its symmetry group. In this paper, the harmonics are presented for
a spatially compactified Bianchi II cosmological model -- the nilgeometric
model. Based on the group structure of the Bianchi II group (also known as the
Heisenberg group) and the compactified spatial topology, the irreducible
differential regular representations and the multiplicity of each irreducible
representation, as well as the explicit form of the harmonics are all
completely determined. They are also extended to vector harmonics. It is
demonstrated that the Klein-Gordon and Maxwell equations actually reduce to
systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM
Electroweak Sudakov Corrections using Effective Field Theory
Electroweak Sudakov corrections of the form alpha^n log^m s/M_{W,Z}^2 are
summed using renormalization group evolution in soft-collinear effective theory
(SCET). Results are given for the scalar, vector and tensor form-factors for
fermion and scalar particles. The formalism for including massive gauge bosons
in SCET is developed.Comment: 5 page
On two theorems for flat, affine group schemes over a discrete valuation ring
We include short and elementary proofs of two theorems characterizing
reductive group schemes over a discrete valuation ring, in a slightly more
general context.Comment: 10 pages. To appear in C. E. J.
Finite-dimensional representations of twisted hyper loop algebras
We investigate the category of finite-dimensional representations of twisted
hyper loop algebras, i.e., the hyperalgebras associated to twisted loop
algebras over finite-dimensional simple Lie algebras. The main results are the
classification of the irreducible modules, the definition of the universal
highest-weight modules, called the Weyl modules, and, under a certain mild
restriction on the characteristic of the ground field, a proof that the simple
modules and the Weyl modules for the twisted hyper loop algebras are isomorphic
to appropriate simple and Weyl modules for the non-twisted hyper loop algebras,
respectively, via restriction of the action
Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)
We investigate a one-parameter family of quantum Harish-Chandra modules of
U_q sl(2n). This family is an analog of the holomorphic discrete series of
representations of the group SU(n,n) for the quantum group U_q su(n, n). We
introduce a q-analog of "the wave" operator (a determinant-type differential
operator) and prove certain covariance property of its powers. This result is
applied to the study of some quotients of the above-mentioned quantum
Harish-Chandra modules. We also prove an analog of a known result by J.Faraut
and A.Koranyi on the expansion of reproducing kernels which determines the
analytic continuation of the holomorphic discrete series.Comment: 26 page
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
On Languages Accepted by P/T Systems Composed of joins
Recently, some studies linked the computational power of abstract computing
systems based on multiset rewriting to models of Petri nets and the computation
power of these nets to their topology. In turn, the computational power of
these abstract computing devices can be understood by just looking at their
topology, that is, information flow.
Here we continue this line of research introducing J languages and proving
that they can be accepted by place/transition systems whose underlying net is
composed only of joins. Moreover, we investigate how J languages relate to
other families of formal languages. In particular, we show that every J
language can be accepted by a log n space-bounded non-deterministic Turing
machine with a one-way read-only input. We also show that every J language has
a semilinear Parikh map and that J languages and context-free languages (CFLs)
are incomparable
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