  We examine a new application of the Holstein-Primakoff realization of the
simple harmonic oscillator Hamiltonian. This involves the use of
infinite-dimensional representations of the Lie algebra $su(2)$. The
representations contain nonstandard raising and lowering operators, which are
nonlinearly related to the standard $a^{\dag}$ and $a$. The new operators also
give rise to a natural family of two-oscillator couplings. These nonlinear
couplings are not generally self-adjoint, but their low-energy limits are
self-adjoint, exactly solvable, and stable. We discuss the structure of a
theory involving these couplings. Such a theory might have as its
ultra-low-energy limit a Lorentz-violating Abelian gauge theory, and we discuss
the extremely strong astrophysical constraints on such a model.
