  A harmonic oscillator is an indefinite-frequency one if the parameter
$\omega$ is replaced by an operator. An ensemble of $N$ such oscillators may be
regarded as a toy model of a bosonic quantum field. All the possible
frequencies associated with a given problem are present already in a single
oscillator and $N$ can be finite. Due to the operator character of $\omega$ the
resulting algebra of creation-annihilation operators is non-canonical. In the
limit of large $N$ one recovers perturbation theory formulas of the canonical
quantum field theory but with form factors automatically built in. Vacuum
energy of the ensemble is finite, a fact discussed in the context of the
cosmological constant problem. Space of states is given by a vector bundle with
Fock-type fibers. Interactions of the field with 2-level systems, including
Rabi oscillations and spontaneous emission, are discussed in detail.
