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General properties of the Yang-Mills equations in physical space.
MedLine Citation:
PMID:  16592565     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Abstract/OtherAbstract:
With the formulation of the gauge group as a Banach-Lie group of suitable Sobolev type, the Cauchy problem for the Yang-Mills equation in physical space-time reduces rigorously to the case of the temporal gauge. In this gauge there exist spatially global strong solutions for given data for field and potential that are L(2) together with one or two derivatives (respectively). Regarding global existence in time, there is strong unicity, strong existence unless the potential becomes unbounded, and existence of a quasi-solution for arbitrary finite-energy Cauchy data. The variety of solutions of the equations is endowed with a canonical symplectic structure. This structure is degenerate to an extent precisely reflecting gauge-invariance and is conformally invariant.
Authors:
I E Segal
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Proceedings of the National Academy of Sciences of the United States of America     Volume:  75     ISSN:  0027-8424     ISO Abbreviation:  Proc. Natl. Acad. Sci. U.S.A.     Publication Date:  1978 Oct 
Date Detail:
Created Date:  2010-06-29     Completed Date:  2010-06-29     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7505876     Medline TA:  Proc Natl Acad Sci U S A     Country:  United States    
Other Details:
Languages:  eng     Pagination:  4638-9     Citation Subset:  -    
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
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