21 research outputs found
The Double Pentaladder Integral to All Orders
We compute dual-conformally invariant ladder integrals that are capped off by
pentagons at each end of the ladder. Such integrals appear in six-point
amplitudes in planar N=4 super-Yang-Mills theory. We provide exact,
finite-coupling formulas for the basic double pentaladder integrals as a single
Mellin integral over hypergeometric functions. For particular choices of the
dual conformal cross ratios, we can evaluate the integral at weak coupling to
high loop orders in terms of multiple polylogarithms. We argue that the
integrals are exponentially suppressed at strong coupling. We describe the
space of functions that contains all such double pentaladder integrals and
their derivatives, or coproducts. This space, a prototype for the space of
Steinmann hexagon functions, has a simple algebraic structure, which we
elucidate by considering a particular discontinuity of the functions that
localizes the Mellin integral and collapses the relevant symbol alphabet. This
function space is endowed with a coaction, both perturbatively and at finite
coupling, which mixes the independent solutions of the hypergeometric
differential equation and constructively realizes a coaction principle of the
type believed to hold in the full Steinmann hexagon function space.Comment: 70 pages, 3 figures, 4 tables; v2, minor typo corrections and
clarification
Spin observables and spin structure functions: inequalities and dynamics
Model-independent identities and inequalities relating the various spin
observables of a reaction are reviewed in a unified formalism, together with
their implications for dynamical models, their physical interpretation, and the
quantum aspects of the information carried by spins, in particular
entanglement. These constraints between observables can be obtained from the
explicit expression of the observables in terms of a set of amplitudes, a
non-trivial algebraic exercise which can be preceded by numerical simulation
with randomly chosen amplitudes, from anticommutation relations, or from the
requirement that any polarisation vector is less than unity. The most powerful
tool is the positivity of the density matrices describing the reaction or its
crossed channels, with a projection to single out correlations between two or
three observables. For the exclusive reactions, the cases of the
strangeness-exchange proton-antiproton scattering and the photoproduction of
pseudoscalar mesons are treated in some detail: all triples of observables are
constrained, and new results are presented for the allowed domains. The
positivity constraints for total cross-sections and single-particle inclusive
reactions are reviewed, with application to spin-dependent structure functions
and parton distributions. The corresponding inequalities are shown to be
preserved by the evolution equations of QCD.Comment: 135 pages, 37 figures, pdflatex, to appear in Physics Reports, new
subsections added, typos corrected, references adde
Integrability, Recursion Operators and Soliton Interactions
This volume contains selected papers based on the talks,presented at the Conference "Integrability, Recursion Operators and Soliton Interactions", held in Sofia, Bulgaria (29 - 31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. The main topics of the conference were those where Vladimir has contributed enormously during his career: integrable nonlinear partial differential equations, underlying algebraic and geometric structures of the integrable systems, soliton solutions, soliton interactions, quantum integrable systems, discrete integrable systems and applications of the nonlinear models. The papers, included in this volume will be useful to researchers with interests in these areas
This Week's Finds in Mathematical Physics (1-50)
These are the first 50 issues of This Week's Finds of Mathematical Physics,
from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity,
topological quantum field theory, knot theory, and applications of
-categories to these subjects. However, there are also digressions into Lie
algebras, elliptic curves, linear logic and other subjects. They were typeset
in 2020 by Tim Hosgood. If you see typos or other problems please report them.
(I already know the cover page looks weird).Comment: 242 page
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group