Exact Results in Statistical Mechanics

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9305930 Goldstein The investigator intends to continue his analysis of Bohmian mechanics, which defines a deterministic dynamical system involving a novel combination of ordinary and partial differential equations having remarkable properties. The proposed research involves the analysis of several rather distinct components: 1) the basic mathematical properties of the system itself, such as existence and uniqueness of the dynamics; 2) phenomenology, such as the emergence of the quantum formalism and of the classical limit; and 3) extensions to relativity and covariant gravitation. %%% The importance of the proposed research lies in the following observations. 1) The foundations of quantum theory continue to be mired in confusion and incoherence some sixty five years after its inception. 2) Bohmian mechanics is the natural embedding of Schroedinger's equation -- the mathematical core of almost all interpretations of quantum theory -- into a clear, precise physical theory, emerging if one merely insists that the Schroedinger wave function be relevant to the motion of particles. 3) An appreciation of Bohmian mechanics can be the source of flexibility and clarity when one attempts to apply quantum theory in new directions -- for example, to understand the implications of macroscopic interference effects -- and to new domains, such as quantum gravity. ***