According to another, conflicting reconstruction, Poincaré invariance is a reality condition; but this applies only to the entire system of fields, not to individual particles. Therefore it ought not constrain the possibility spaces of individual particles.
Consequently, I argue, we have reason to consider "larger" state spaces than are normally considered. On one such approach, which I will advocate, the elements of these state spaces represent entire four-dimensional histories rather than instantaneous states---most of which are "off mass-shell", in that the relativistic mass condition is violated. I conclude by arguing that off-mass-shell particles, far from being mere formal inventions for the sake of S-matrix calculations, are just as "real" as their free counterparts---indeed, they are to be found as much in classical relativistic theories as in quantum relativistic theories.
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