Determining and uniformly estimating the gauge potential corresponding to a given gauge field on \(M^ 4\)
type: Item
instance of: scholarly article
title: Determining and uniformly estimating the gauge potential corresponding to a given gauge field on \(M^ 4\)
zbMATH Open document ID: 0603.58046
DOI: 10.1007/BF00416466
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: In an earlier paper on the field copy problem, we proved that there exists a generic set of connections (gauge potentials) on a principle bundle with a semi-simple structure group over a four-dimensional base manifold for which the connection is uniquely determined by its curvature (gauge fields). We conjectured that there exists a smaller, but still generic, set of connections for which the curvature map sending a connection to its curvature admits a continuous inverse with respect to the appropriate function space topologies. The conjecture says, in other words, that restricting to certain generic curvature 2-forms, one can determine and uniformly estimate the connection and its derivatives from the curvature and uniform estimates of its derivatives. In this Letter we give an affirmative answer to the conjecture and show, moreover, that the set of such connections contains an open dense set in the Whitney \(C^{\infty}\) topology.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3973917
zbMATH Keywords: gauge potentials
zbMATH Keywords: principle bundle
zbMATH Keywords: semi-simple structure group
zbMATH Keywords: generic curvature 2-forms
zbMATH Keywords: Whitney \(C^{\infty }\) topology
author: Mark A. Mostow
author: Steven Shnider
MaRDI profile type: Publication
cites work: Does a generic connection depend continuously on its curvature?
cites work: Joint Continuity of Division of Smooth Functions. I: Uniform Lojasiewicz Estimates
cites work: Joint Continuity of Division of Smooth Functions. II: The Distance to a Whitney Stratified Set from a Transversal Submanifold
cites work: Q4046802
cites work: Stability of transversality to a stratification implies Whitney (a)- regularity
description: scientific article; zbMATH DE number 3973917