Regularity and energy quantization for the Yang-Mills-Dirac equations on 4-manifolds. (English) Zbl 1225.58007
The author considers a Yang-Mills-Dirac equation on 4-dimensional Riemannian manifolds and shows that any of its finite energy weak solutions is regular in the sense that it is \(W^{2,2}\cap C^0\)-gauge equivalent to a \(C^\infty\)-solution. Moreover, a compactness-energy quantization effect for the Yang-Mills-Dirac equation is observed and discussed. Interesting arguments involving interpolation spaces and the regularity properties of basic differential operators acting on these interpolation space are used.
Reviewer: Wojciech Kryszewski (Toruń)
MSC:
| 58E15 | Variational problems concerning extremal problems in several variables; Yang-Mills functionals |
| 49N60 | Regularity of solutions in optimal control |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
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