Related papers: Constructive aspects of algebraic euclidean field …
We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular…
We survey the use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature. The Calkin algebra emerges as a basic object of interest.
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…
This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…
We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…
We propose to study some properties of the $C^*$-algebra naturally built out of the fundamental action that an automaton group $G$ admits on a regular rooted trees $\tree$.
A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general…
We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
In this article, we develop an algebraic framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. We further construct an explicit model and prove that it satisfies…
We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
The paper provides an introduction to the field of Algebraic Set Theory (AST). AST is a flexible categorical framework for studying different kinds of set theories: both classical and constructive, predicative and impredicative. We discuss…
We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as compact formulations by using the polar decomposition of the complex link fields.…
The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the…
We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…