Exact Results in Statistical Mechanics

小行星9305930 研究人员打算继续他的分析Bohmian力学，它定义了一个确定性的动力系统，涉及一个新的组合的普通和偏微分方程具有显着的性质。 拟议的研究涉及几个相当不同的组成部分的分析：1）系统本身的基本数学性质，如动力学的存在性和唯一性; 2）现象学，如量子形式主义和经典极限的出现;和3）相对论和协变引力的扩展。 %%% 拟议研究的重要性在于以下观察结果。 1)量子理论的基础在创立65年后仍然陷于混乱和不连贯之中。 2)玻姆力学是薛定谔方程的自然嵌入-几乎所有量子理论解释的数学核心-成为一个清晰，精确的物理理论，如果人们仅仅坚持薛定谔波函数与粒子运动有关，就会出现。 3)当人们试图将量子理论应用于新的方向时，对玻姆力学的理解可以是灵活性和清晰度的来源-例如，理解宏观干涉效应的含义-以及新的领域，如量子引力。 ***

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. ***