论文标题
牛顿后对重力领域量子系统的描述
Post-Newtonian Description of Quantum Systems in Gravitational Fields
论文作者
论文摘要
本论文涉及牛顿后重力场中量子力学系统的系统处理。从明确的拼写假设开始，采用定义纽顿后扩展概念的几何背景结构的框架，我们的系统方法允许根据第一原理正确地得出量子机械系统的量子机械系统的纽顿后耦合。这使它与普遍使用的更多启发式方法（例如在重力下的量子光学实验描述中）区分开来。 关于单个粒子，我们将弯曲时空中游离粒子的简单典型定量与最小耦合的klein-gordon方程的形式膨胀进行了比较，这可能是在弯曲的空间中从QFT中动机的。具体而言，我们开发了一个像WKB的一般后纽顿后扩展，将kg方程式扩展到$ c^{ - 1} $中的任意顺序。此外，对于固定的空间，我们表明，由kg方程的扩展和规范定量产生的汉密尔顿人同意粒子动量的线性顺序，与$ c^{ - 1} $中的任何扩展无关。 关于复合系统，我们对Newtonian Quantum Hamiltonian的第一阶进行了完全详细的系统推导，描述了位于外部电磁和引力场中的电磁结合的两粒子系统的动力学，后者由Eddington-Robertson PPN PPN Metric描述。 在论文的最后一个独立的部分中，我们证明了牛顿的两个独特性结果 - 牛顿的定位 - 对庞加莱的不变性古典哈密顿量系统：一个是纽顿量子牛顿定理的直接古典类似物，以及其他澄清的牛顿 - 温顿 - 温顿 - 温顿 - 温顿（Newton-Wigner）的几何解释。
This thesis deals with the systematic treatment of quantum-mechanical systems in post-Newtonian gravitational fields. Starting from clearly spelled-out assumptions, employing a framework of geometric background structures defining the notion of a post-Newtonian expansion, our systematic approach allows to properly derive the post-Newtonian coupling of quantum-mechanical systems to gravity based on first principles. This sets it apart from more heuristic approaches that are commonly employed, for example, in the description of quantum-optical experiments under gravity. Regarding single particles, we compare simple canonical quantisation of a free particle in curved spacetime to formal expansions of the minimally coupled Klein-Gordon equation, which may be motivated from QFT in curved spacetimes. Specifically, we develop a general WKB-like post-Newtonian expansion of the KG equation to arbitrary order in $c^{-1}$. Furthermore, for stationary spacetimes, we show that the Hamiltonians arising from expansions of the KG equation and from canonical quantisation agree up to linear order in particle momentum, independent of any expansion in $c^{-1}$. Concerning composite systems, we perform a fully detailed systematic derivation of the first order post-Newtonian quantum Hamiltonian describing the dynamics of an electromagnetically bound two-particle system situated in external electromagnetic and gravitational fields, the latter being described by the Eddington-Robertson PPN metric. In the last, independent part of the thesis, we prove two uniqueness results characterising the Newton--Wigner position observable for Poincaré-invariant classical Hamiltonian systems: one is a direct classical analogue of the quantum Newton--Wigner theorem, and the other clarifies the geometric interpretation of the Newton--Wigner position as `centre of spin', as proposed by Fleming in 1965.
