Yang-Mills and Dirac Fields in a Bag, Existence and Uniqueness Theorems

Schwarz, Günter ; Sniatycki, Jedrzej

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URL: https://ub-madoc.bib.uni-mannheim.de/1654
URN: urn:nbn:de:bsz:180-madoc-16549
Document Type: Working paper
Year of publication: 1994
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 81E13 35F25 ,
Subject headings (SWD): Dirac-Gleichung , Yang-Mills-Theorie
Keywords (English): Dirac equation , Yang-Mills equations , non-linear evolution equations , bag boundary conditions
Abstract: The Cauchy problem for the Yang-Mills-Dirac system with minimal coupling is studied under the MIT quark bag boundary conditions. An existence and uniqueness theorem for the free Dirac equation is proven under that boundary condition. The existence and uniqueness of the classical time evolution of the Yang-Mills-Dirac system in a bag is shown. To ensure sufficient differentiability of the fields we need additional boundary conditions. In the proof we use the Hodge decomposition of Yang-Mills fields and the theory of non-linear semigroups.
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