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We present a classification and an explicit form of all constant solutions of the Yang–Mills equations with SU (2) gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ℝ p , q of arbitrary finite dimension n = p + q. Using hyperbolic singular value decomposition and two-sheeted covering of orthogonal group by spin group, we solve the nontrivial system for constant solutions of the Yang–Mills equations of 3 n cubic equations with 3 n unknowns and 3 n parameters in the general case. We present a new symmetry of this system of equations. All solutions in terms of the potential, strength and invariant of the Yang–Mills field are presented. Nonconstant solutions of the Yang–Mills equations can be considered in the form of series of perturbation theory using all constant solutions as a zeroth approximation. [ABSTRACT FROM AUTHOR]

Explicit, analytic and closed expressions for boson realizations of the (m+3)-parameter nonlinearly deformed angular momentum algebra {R}{r, s}(m) with its highest power m of polynomial function being arbitrary, which combines and generalizes Witten's two deformation schemes, are investigated in terms of the single boson and the single inversion boson, respectively. For each kind, the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-Maléev-like realization and their connections are respectively discussed. Using these realizations, the corresponding representations of {R}{r, s}(m) as well as their respective acting spaces in the Fock space are obtained. [ABSTRACT FROM AUTHOR]