21,562 research outputs found
Classical String in Curved Backgrounds
The Mathisson-Papapetrou method is originally used for derivation of the
particle world line equation from the covariant conservation of its
stress-energy tensor. We generalize this method to extended objects, such as a
string. Without specifying the type of matter the string is made of, we obtain
both the equations of motion and boundary conditions of the string. The world
sheet equations turn out to be more general than the familiar minimal surface
equations. In particular, they depend on the internal structure of the string.
The relevant cases are classified by examining canonical forms of the effective
2-dimensional stress-energy tensor. The case of homogeneously distributed
matter with the tension that equals its mass density is shown to define the
familiar Nambu-Goto dynamics. The other three cases include physically relevant
massive and massless strings, and unphysical tahyonic strings.Comment: 12 pages, REVTeX 4. Added a note and one referenc
PORTFOLIO ANALYSIS CONSIDERING ESTIMATION RISK AND IMPERFECT MARKETS
Mean-variance efficient portfolio analysis is applied to situations where not all assets are perfectly price elastic in demand nor are asset moments known with certainty. Estimation and solution of such a model are based on an agricultural banking example. The distinction and advantages of a Bayesian formulation over a classical statistical approach are considered. For maximizing expected utility subject to a linear demand curve, a negative exponential utility function gives a mathematical programming problem with a quartic term. Thus, standard quadratic programming solutions are not optimal. Empirical results show important differences between classical and Bayesian approaches for portfolio composition, expected return and measures of risk.Agricultural Finance, Research Methods/ Statistical Methods,
All-Orders Singular Emission in Gauge Theories
I present a class of functions unifying all singular limits for the emission
of soft or collinear gluons in gauge-theory amplitudes at any order in
perturbation theory. Each function is a generalization of the antenna functions
of ref. [1]. The helicity-summed interferences these functions are thereby also
generalizations to higher orders of the Catani--Seymour dipole factorization
function.Comment: 5 pages, 1 figur
1-loop matching and NNLL resummation for all partonic 2 to 2 processes in QCD
The Wilson Coefficients for all 4-parton operators which arise in matching
QCD to Soft-Collinear Effective Theory (SCET) are computed at 1-loop. Any dijet
observable calculated in SCET beyond leading order will require these results.
The Wilson coefficients are separated by spin and color, although most
applications will involve only the spin-averaged hard functions. The anomalous
dimensions for the Wilson coefficients are given to 2-loop order, and the
renormalization group equations are solved explicitly. This will allow for
analytical resummation of dijet observables to next-to-next-to-leading
logarithmic accuracy. For each channel, there is a natural basis in which the
evolution is diagonal in color space. The same basis also diagonalizes the
color evolution for the soft function. Even though soft functions required for
SCET calculations are observable dependent, it is shown that their
renormalization group evolution is almost completely determined by a universal
structure. With these results, it will be possible to calculate hadronic event
shapes or other dijet observables to next-to-leading order with
next-to-next-to-leading log resummation.Comment: 28 pages, 5 tables; v2: typo corrected in Eq. (56
The Last of the Finite Loop Amplitudes in QCD
We use on-shell recursion relations to determine the one-loop QCD scattering
amplitudes with a massless external quark pair and an arbitrary number (n-2) of
positive-helicity gluons. These amplitudes are the last of the unknown
infrared- and ultraviolet-finite loop amplitudes of QCD. The recursion
relations are similar to ones applied at tree level, but contain new
non-trivial features corresponding to poles present for complex momentum
arguments but absent for real momenta. We present the relations and the compact
solutions to them, valid for all n. We also present compact forms for the
previously-computed one-loop n-gluon amplitudes with a single negative helicity
and the rest positive helicity.Comment: 45 pages, revtex, 7 figures, v2 minor correction
Spin-Dependent Antenna Splitting Functions
We consider parton showers based on radiation from QCD dipoles or `antennae'.
These showers are built from 2->3 parton splitting processes. The question then
arises of what functions replace the Altarelli-Parisi splitting functions in
this approach. We give a detailed answer to this question, applicable to
antenna showers in which partons carry definite helicity, and to both initial-
and final-state emissions.Comment: 31 pages, 12 figure
A Color Dual Form for Gauge-Theory Amplitudes
Recently a duality between color and kinematics has been proposed, exposing a
new unexpected structure in gauge theory and gravity scattering amplitudes.
Here we propose that the relation goes deeper, allowing us to reorganize
amplitudes into a form reminiscent of the standard color decomposition in terms
of traces over generators, but with the role of color and kinematics swapped.
By imposing additional conditions similar to Kleiss-Kuijf relations between
partial amplitudes, the relationship between the earlier form satisfying the
duality and the current one is invertible. We comment on extensions to loop
level.Comment: 5 pages, 4 figure
Generalizing Boolean Satisfiability I: Background and Survey of Existing Work
This is the first of three planned papers describing ZAP, a satisfiability
engine that substantially generalizes existing tools while retaining the
performance characteristics of modern high-performance solvers. The fundamental
idea underlying ZAP is that many problems passed to such engines contain rich
internal structure that is obscured by the Boolean representation used; our
goal is to define a representation in which this structure is apparent and can
easily be exploited to improve computational performance. This paper is a
survey of the work underlying ZAP, and discusses previous attempts to improve
the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting
the structure of the problem being solved. We examine existing ideas including
extensions of the Boolean language to allow cardinality constraints,
pseudo-Boolean representations, symmetry, and a limited form of quantification.
While this paper is intended as a survey, our research results are contained in
the two subsequent articles, with the theoretical structure of ZAP described in
the second paper in this series, and ZAP's implementation described in the
third
New relations for scattering amplitudes in Yang-Mills theory at loop level
The calculation of scattering amplitudes in Yang-Mills theory at loop level
is important for the analysis of background processes at particle colliders as
well as our understanding of perturbation theory at the quantum level. We
present tools to derive relations for especially one loop amplitudes, as well
as several explicit examples for gauge theory coupled to a wide variety of
matter. These tools originate in certain scaling behavior of permutation and
cyclic sums of Yang-Mills tree amplitudes and loop integrands. In the latter
case evidence exists for relations at all loop orders.Comment: 12 pages, 4 figures. v3: typos corrected, figures and clarifications
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BRS Cohomology of the Supertranslations in D=4
Supersymmetry transformations are a kind of square root of spacetime
translations. The corresponding Lie superalgebra always contains the
supertranslation operator . We find that the
cohomology of this operator depends on a spin-orbit coupling in an SU(2) group
and has a quite complicated structure. This spin-orbit type coupling will turn
out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9
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