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Positive-energy solutions of the Klein-Gordon equation form a Hilbert spaceof holomorphic functions on the future tube. This domain is interpreted as anextended phase space for the associated classical particle, the extradimensions being the time and a new variable related to the inverse equilibriumtemperature in an associated canonical ensemble. This gives a compellingformulation of relativistic Bohmian mechanics where the "hidden variables" aresimply the classical trajectories of the particle in phase space. Interactionsmay be included through "holomorphic gauge theory."

Thermal Spacetime, Part I: Relativistic Bohmian Mechanics