I am going through Ramond's 1971 paper Dual Theory for Free Fermions Phys Rev D3 10, 2415 where he first attempts to introduce fermions into the conventional dual resonance model.
I get the 'gist' of what he's doing: he draws an analogy of the bosonic oscillators satisfying the Klein-Gordon equation, and extends it to incorporate some version of the Dirac equation. Great.
without resorting to string theory (since I know nothing about it) and perhaps minimally resorting to field theory (after all, this is still S-matrix theory, right?), how can I understand his correspondence principle (eqn 3)?
$$p^2-m^2=\langle P\rangle\!\cdot\!\langle P\rangle-m^2\rightarrow\langle P\!\cdot\! P\rangle-m^2$$
(the same correspondence principle appears in Frampton's 1986 book "Dual Resonance Models" equation 5.63). Is this a special property of harmonic oscillators?