We revisit the principal arguments for interpreting the free quantum fields
on anti-de Sitter or de Sitter spacetimes of any dimensions as oscillators or
respectively anti-oscillators. In addition, we point out that there exists a
chart on the de Sitter background where the free Dirac field becomes a genuine
anti-oscillator in the non-relativistic limit in the sense of special
relativity.Comment: 7 pages, no figure