Related papers: Cutting-Edge Tools for Cutting Edges
It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points…
In this work, we study the realisation of unitarity-based cutting rules for primordial cosmological correlators computed within the Schwinger-Keldysh path integral formalism. While cutting rules have been previously derived for wavefunction…
Scattering amplitudes in the high-energy limit can be described in terms of their singularity structure in the complex angular momentum plane, consisting of Regge poles and cuts. In QCD, gluon Reggeization has long been understood as a…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
This thesis is concerned with the study of scattering amplitudes in four-dimensional conformal field theories, more particularly the N=4 super-Yang-Mills theory. We study this theory first at tree level by using twistor space techniques and…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
The $N/D$ method is used to study the $S_{11}$ channel low energy $\pi N$ scattering amplitude. The input of left cuts are obtained from various phenomenological models. With the aid of the production representation, the total phase shifts…
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
We introduce a natural notion of depth that applies to individual cutting planes as well as entire families. This depth has nice properties that make it easy to work with theoretically, and we argue that it is a good proxy for the practical…
The quantum effects encapsulated in loop corrections are crucial in quantum field theory for a wide variety of formal and phenomenological applications. In this article we propose and check a definition of the so-called single cut…
We present an overview of recent developments, based on on-shell techniques, in the calculation of multi-parton scattering amplitudes at one loop that are relevant for phenomenological studies at hadron colliders. These new on-shell methods…
I describe how to calculate cross sections for hard-scattering processes in high energy collisions at next to leading order in QCD. I consider infrared-safe quantities and I assume that the scattering amplitudes are known in analytic form…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of well known invariance of scattering matrix with respect to the field transformation of the…
This lecture aims at providing a user's perspective on the main concepts used nowadays for the implementation of numerical algorithm on common computing architecture. In particular, the concepts and applications of Central Processing Units…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called {\em…
Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with…
Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…