Thin homotopy and the holonomy approach to gauge theories

DOI10.1090/conm/775/15594zbMath1495.53071arXiv1904.10822OpenAlexW3216336266MaRDI QIDQ5085342

Cláudio N. Meneses

Publication date: 27 June 2022

Published in: Mexican Mathematicians in the World (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.10822

zbMATH Keywords

holonomygauge fieldthin homotopy

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Issues of holonomy in differential geometry (53C29) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02) Geometries with differentiable structure (51H25)

Cites Work

• Parallel transport on principal bundles over stacks
• A Poincaré lemma for connection forms
• Construction of universal bundles. II
• Classification of fibre bundles by the loop space of the base
• Quantum electrodynamics without potentials
• Holonomy and path structures in general relativity and Yang-Mills theory
• Parallel transport and functors
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• Characteristic numbers of \(U_ 1\)-valued lattice gauge fields
• Lattice gauge fields, principal bundles and the calculation of topological charge
• Holonomy and gravity
• Classifications of bundle connection pairs by parallel translation and lassos
• Non-abelian Stokes formula
• On the bundle of connections and the gauge orbit manifold in Yang-Mills theory
• Gauge groups and classification of bundles with simple structural group
• Bundle-connection pairs and loop group representations
• The extended loop group: An infinite dimensional manifold associated with the loop space
• Connections on the path bundle of a principal fiber bundle
• Reconstruction theorem for groupoids and principal fiber bundles
• Functional integration on spaces of connections
• Regular connections among generalized connections
• Axiomatic holonomy maps and generalized Yang-Mills moduli space
• Loop and path spaces and four-dimensional \(BF\) theories: connections, holonomies and observables
• Topology of lattice gauge fields
• Holonomy and parallel transport for abelian gerbes
• On the support of the Ashtekar-Lewandowski measure
• Differential geometry on the space of connections via graphs and projective limits
• Sur les connexions infinitésimales qu'on peut définir dans les structures fibrées différentiables de base donnée
• Iterated integrals of differential forms and loop space homology
• The computation of characteristic classes of lattice gauge fields
• Homotopy classes of gauge fields and the lattice
• CHEN INTEGRALS, GENERALIZED LOOPS AND LOOP CALCULUS
• On the Ashtekar-Lewandowski measure as a restriction of the product one
• THE SMOOTH STRUCTURE OF THE SPACE OF PIECEWISE-SMOOTH LOOPS
• On two-dimensional holonomy
• Completeness of Wilson loop functionals on the moduli space of SL(2,C) and SU(1,1) connections
• Group of loops, holonomy maps, path bundle and path connection
• A topological Chern-Weil theory
• Significance of Electromagnetic Potentials in the Quantum Theory
• Yang-Mills Connections on Surfaces and Representations of the Path Group
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Integral Formalism for Gauge Fields
• Representations of the holonomy algebras of gravity and nonAbelian gauge theories
• Iterated path integrals
• AN AXIOMATIC DEFINITION OF HOLONOMY
• Quantised singularities in the electromagnetic field,
• On the Loop Space Formulation of Gauge Theories
• Extended loops: A new arena for nonperturbative quantum gravity
• Macroscopic observables from the comparison of local reference systems
• Comparative Smootheology
• Non-covariance of the generalized holonomies: Examples
• Constructing smooth manifolds of loop spaces
• "Parallel" transport - revisited
• Généralisation du groupe fondamental
• Existence of Universal Connections
• Homotopy Equivalence of Fiber Bundles
• On the holonomic equivalence of two curves
• Groups of loops and hoops
• Stratification of the generalized gauge orbit space
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Thin homotopy and the holonomy approach to gauge theories