Related papers: Yang-Mills Meets Data

In a previous publication [1], local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can…

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behavior of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from…

We continue the study of fuzzy geometries inside Connes' spectral formalism and their relation to multimatrix models. In this companion paper to [arXiv 2007:10914, Ann. Henri Poincar\'e] we propose a gauge theory setting based on…

In this paper, we provide the notions of connection $1$-forms and curvature $2$-forms on graphs. We prove a Weitzenb\"ock formula for connection Laplacians in this setting. We also define a discrete Yang-Mills functional and study its…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…

I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main…

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

High-energy phenomena presenting strong dynamical correlations, long-range interactions and microscopic memory effects are well described by nonextensive versions of the canonical Boltzmann-Gibbs statistical mechanics. After a brief…

We suggest that four dimensional massive gauge vectors could be described by coupling ordinary Yang-Mills theory to a topological gauge theory. For this the coupling should excite a nontrivial degree of freedom from the topological theory,…

Generalized Yang-Mills theories are constructed, that can use fields other than vector as gauge fields. Their geometric interpretation is studied. An application to the Glashow-Weinberg-Salam model is briefly review, and some related…

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating…

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…

The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…

The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…

We introduce new local gauge invariant variables for N=1 supersymmetric Yang-Mills theory, explicitly parameterizing the physical Hilbert space of the theory. We show that these gauge invariant variables have a geometrical interpretation,…

Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In this paper, by comparing the geometric structure of…