Gauge-natural bundles and generalized gauge theories
The concept of gauge-natural bundles is introduced. They are a generalization of natural bundles and they provide a natural formal context for the discussion of gauge field theories. It is shown that such bundles correspond to actions of certain Lie groups on smooth manifolds and that natural differential operators between them correspond to equivariant maps. Some results of classical gauge theory are reformulated and reproved in the language of gauge-natural bundles, including a theorem of Uti…
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- Full title :Gauge-natural bundles and generalized gauge theories / by David J. Eck.
Summary
The concept of gauge-natural bundles is introduced. They are a generalization of natural bundles and they provide a natural formal context for the discussion of gauge field theories. It is shown that such bundles correspond to actions of certain Lie groups on smooth manifolds and that natural differential operators between them correspond to equivariant maps. Some results of classical gauge theory are reformulated and reproved in the language of gauge-natural bundles, including a theorem of Utiyama which describes first order gauge-invariant Lagrangians on the bundle of connections of a principal bundle.
Read More ↓Edition Statements
- Publication Date:©1981.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©1981.
The Physical Object
- Description:vi, 48 pages ; : 26 cm.
Edition Identifiers
- ISBN:0821822470, 9780821822470
- oclc:ocm07738383
- LC Classification:QA3
- Dewey Decimal:510 s
Table of Contents
Introduction -- The functors (·)[superscript italic]n[over][subscript italic]k -- The groups [italic]A[superscript italic]n[over][subscript italic]r, [subscript italic]s([italic]G) -- Gauge-natural bundles and differential operators between them -- Examples; relationship to classical theory -- Gauge-invariant Lagrangians.
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