  Positive-energy solutions of the Klein-Gordon equation form a Hilbert space
of holomorphic functions on the future tube. This domain is interpreted as an
extended phase space for the associated classical particle, the extra
dimensions being the time and a new variable related to the inverse equilibrium
temperature in an associated canonical ensemble. This gives a compelling
formulation of relativistic Bohmian mechanics where the "hidden variables" are
simply the classical trajectories of the particle in phase space. Interactions
may be included through "holomorphic gauge theory."
