Related papers: Higher Gauge Theory
In this expository article, we summarize what is known about maximum likelihood thresholds of Gaussian models, paying special attention to connections with rigidity theory.
Some principal problems of general relativity theory and attempts of their solution are discussed. The Poincare gauge theory of gravity as natural generalization of Einsteinian gravitation theory is considered. The changes of gravitational…
Ideas about a duality between gauge fields and strings have been around for many decades. During the last ten years, these ideas have taken a much more concrete mathematical form. String descriptions of the strongly coupled dynamics of…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
We survey recent progress in understanding the relation of string theory to quantum chromodynamics, focusing on holographic models of gauge theories similar to QCD and applications to heavy-ion collisions.
Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy…
This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N=4 super-Yang-Mills theory, as well as (super)gravity. I also…
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…
We formulate a new model which describes higher-spin gauge interactions for matter fields in two dimensions. This model is a higher-spin generalization of d2 gravity and turns out to be integrable. No vanishing higher-spin current…
Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…
A book Chapter consisting of some of the main areas of research in graph theory applied to physics. It includes graphs in condensed matter theory, such as the tight-binding and the Hubbard model. It follows the study of graph theory and…
Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
We review recent developments in holographic hydrodynamics. We start from very basic discussion on hydrodynamic systems and motivate why string theory is an essential tool to deal with these systems when they are strongly coupled. The main…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…