Related papers: Why surplus structure is not superfluous
Perturbative superstring theory is revisited, with the goal of giving a simpler and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from known anomalies), satisfy space-time supersymmetry when expected, and…
A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle…
We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The…
The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…
We discuss the nature of structure and organization, and the process of making new Things. Hyperstructures are introduced as binding and organizing principles, and we show how they can transfer from one situation to another. A guiding…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
We discuss the gauge theory mechanisms which are responsible for the causal structure of the dual supergravity. For D-brane probes we show that the light cone structure and Killing horizons of supergravity emerge dynamically. They are…
In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects,…
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
In this article we survey some of the recent developments in the structure theory of set addition.
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. The starting point of this research was the need to understand in a sound mathematical framework some…
The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translation in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory,…
Furstenberg--Zimmer structure theory refers to the extension of the dichotomy between the compact and weakly mixing parts of a measure preserving dynamical system and the algebraic and geometric descriptions of such parts to a conditional…
By an additive structure on a hypersurface S in projective space we mean an effective action of commutative unipotent group on projective space which leaves S invariant and acts on S with an open orbit. It is known that these structures…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec.…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions…
We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…