Counterexamples to some results on the existence of field copies

Mark A. Mostow, Steven Shnider

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Several criteria are known for determining which connections A are determined uniquely by their curvature F, or by F and its covariant derivatives. On a principal bundle with semi-simple gauge group G over a 4-manifold M, a sufficient condition for F to determine A uniquely is that the linear map B → [F ∧B] from Lie algebra-valued 1-forms to 3-forms (pulled back to M via a local gauge) be invertible on an open dense set in M. Recently F. A. Doria has claimed that this condition is also necessary. We present counterexamples to this claim, and also to his assertion that F determines A uniquely if the restriction of the bundle to every open subset of M has holonomy group equal to G and F is "not degenerate as a 2-form over spacetime."

Original languageEnglish
Pages (from-to)521-526
Number of pages6
JournalCommunications in Mathematical Physics
Volume90
Issue number4
DOIs
StatePublished - Dec 1983
Externally publishedYes

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