Phase-space approach to relativistic quantum mechanics. I. Coherent-state representation for massive scalar particles

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  • Gerald Kaiser
    Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1

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<jats:p>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.</jats:p>

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