Marchuk, Nikolay; Shirokov, Dmitry Constant solutions of Yang-Mills equations and generalized Proca equations. (English) Zbl 1366.35152 J. Geom. Symmetry Phys. 42, 53-72 (2016). 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. Cited in 6 Documents 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 Keywords:Clifford and Grassmann algebras; Proca equation; Yang-Mills equations × Cite Format Result Cite Review PDF Full Text: DOI arXiv