Abstract
We construct a family of equivalent representations Uλ (λ≳0) of the restricted Poincaré group 𝒫↑+ for a massive scalar particle on spaces 𝒦λ of functions defined over ’’phase space’’ Pλ. Each Pλ is a submanifold of the forward tube, and 𝒦λ consists of restrictions on holomorphic solutions of the Klein–Gordon equation to Pλ. Each 𝒦λ has a resolution of the identity in terms of ’’coherent states’’ ez, zεPλ, which are wavepackets characterized by an invariant extremal property.
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