Thermal Spacetime, Part I: Relativistic Bohmian Mechanics

Abstract

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."

30 pages, 3 figures