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Constant solutions of Yang-Mills equations and generalized Proca equations. (English) Zbl 1366.35152

Summary: Here we present some new equations which we call Yang-Mills-Proca equations (or generalized Proca equations). This system of equations is a generalization of Proca equation and Yang-Mills equations and it is not gauge invariant. We present a number of constant solutions of this system of equations in the case of arbitrary Lie algebra. We consider in detail the case when this Lie algebra is a Clifford or a Grassmann algebra and derive solutions of Yang-Mills equations in the form of perturbation theory series near the constant solution.

MSC:

35Q40 PDEs in connection with quantum mechanics
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
15A66 Clifford algebras, spinors
15A75 Exterior algebra, Grassmann algebras
81T13 Yang-Mills and other gauge theories in quantum field theory
35Q60 PDEs in connection with optics and electromagnetic theory
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