Related papers: An Introduction to Webs
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like…
These lectures give a pedagogical introduction to real and virtual Compton scattering at low energies. We will first discuss real Compton scattering off a point particle as well as a composite system in the framework of nonrelativistic…
Quantum computing provides a novel avenue towards simulating dynamical phenomena, and, in particular, scattering processes relevant for exploring the structure of matter. However, preparing and evolving particle wave packets on a quantum…
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time…
The concept of the cosmic web, viewing the Universe as a set of discrete galaxies held together by gravity, is deeply engrained in cosmology. Yet, little is known about the most effective construction and the characteristics of the…
Situated as a language between computer science, quantum physics and mathematics, tensor network theory has steadily grown in popularity and can now be found in applications ranging across the entire field of quantum information processing.…
Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. In this paper we go in the opposite direction, using known properties of line arrangements to motivate certain equivalence relations and actions…
Webs give a diagrammatic calculus for spaces of tensor invariants. We introduce hourglass plabic graphs as a new avatar of webs, and use these to give the first rotation-invariant $U_q(\mathfrak{sl}_4)$-web basis, a long-sought object. The…
Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…
Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
Networks have provided extremely successful models of data and complex systems. Yet, as combinatorial objects, networks do not have in general intrinsic coordinates and do not typically lie in an ambient space. The process of assigning an…
A survey is given on the present status of analytic calculation methods and the mathematical structures of zero- and single scale Feynman amplitudes which emerge in higher order perturbative calculations in the Standard Model of elementary…
Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a…
Exponential random graph theory is the complex network analog of the canonical ensemble theory from statistical physics. While it has been particularly successful in modeling networks with specified degree distributions, a naive model of a…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with…