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Zbl 0958.58009
Śniatycki, Jedrzej
Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 70, No.3, 277-293 (1999). ISSN 0246-0211

Summary: The constraint equations for Yang-Mills and Dirac fields are investigated for the extended phase space consisting of the Cauchy data $A\in H^2(\bbfR^3)$, $E\in H^1(\bbfR^3)$, and $\Psi\in H^2(\bbfR^3)$. The solution set is a smooth submanifold of a dense subspace of the extended phase space. It is a principal fibre bundle over the reduced phase space with structure group consisting of the gauge symmetries approaching the identity at infinity.

MSC 2000:: *58E15 Appl. of variational methods to extremal problems in sev.variables

Keywords: Banach manifolds; constraints; nonlinear partial differential equations; reduction; Yang-Mills fields; Dirac fields

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