Abstract
In the framework of the formal theory of overdetermined systems of partial differential equations, it is shown that the Yang-Mills-Higgs equations are an involutive, and hence formally integrable, system. To this end a key role is played by the gauge invariance of the theory and the resulting differential identities involving the field equations themselves. By applying a theorem of Malgrange, an existence theorem for the solutions of the Yang-Mills-Higgs field equations in the analytic context is thus obtained. The approach is within differential geometry.
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Giachetta, G., Mangiarotti, L. Gauge invariance and formal integrability of the Yang-Mills-Higgs equations. Int J Theor Phys 35, 1405–1422 (1996). https://doi.org/10.1007/BF02084950
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DOI: https://doi.org/10.1007/BF02084950