Abstract
The geometry of Yang-Mills fields is placed in the general frame of the Hamilton-Cartán formalism of the Calculus of Variations. The pre-symplectic structure of the space of solutions of the linearization of field equations at one of their solutions is studied. Using results of the Hodge theory for harmonic forms, the radical of the pre-symplectic metric of a Yang-Mills field is determined and conclusions are drawn about the corresponding manifolds of moduli with respect to the gauge group. The procedure to be followed in order to generalize the method to "minimal interactions" is illustrated with an elementary example, and finally some possible ways for further generalizations are pointed out.
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García, P.L. (1980). Tangent structure of Yang-Mills equations and hodge theory. In: García, P.L., Pérez-Rendón, A., Souriau, J.M. (eds) Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089745
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DOI: https://doi.org/10.1007/BFb0089745
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