PostNewtonian Description of Quantum Systems in Gravitational Fields
 verfasst von
 Philip Klaus Schwartz
 betreut von
 Domenico Giulini
 Abstract
This thesis deals with the systematic treatment of quantummechanical systems situated in postNewtonian gravitational fields. At first, we develop a framework of geometric background structures that define the notions of a postNewtonian expansion and of weak gravitational fields. Next, we consider the description of single quantum particles under gravity, before continuing with a simple composite system. Starting from clearly spelledout assumptions, our systematic approach allows to properly derive the postNewtonian coupling of quantummechanical systems to gravity based on first principles. This sets it apart from other, more heuristic approaches that are commonly employed, for example, in the description of quantumoptical experiments under gravitational influence. 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 the framework of quantum field theory in curved spacetimes. Specifically, we develop a general WKB like postNewtonian expansion of the Klein–Gordon equation to arbitrary order in the inverse of the velocity of light. Furthermore, for stationary spacetimes, we show that the Hamiltonians arising from expansions of the Klein–Gordon equation and from canonical quantisation agree up to linear order in particle momentum, independent of any expansion in the inverse of the velocity of light. Concerning the topic of composite systems, we perform a fully detailed systematic derivation of the first order postNewtonian quantum Hamiltonian describing the dynamics of an electromagnetically bound twoparticle system which is situated in external electromagnetic and gravitational fields. This calculation is based on previous work by Sonnleitner and Barnett, which we significantly extend by the inclusion of a weak gravitational field as described by the Eddington–Robertson parametrised postNewtonian metric. In the last, independent part of the thesis, we prove two uniqueness results characterising the Newton–Wigner position observable for Poincaréinvariant classical Hamiltonian systems: one is a direct classical analogue of the wellknown 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.
 Organisationseinheit(en)

Institut für Theoretische Physik
QUEST Leibniz Forschungsschule
 Typ
 Dissertation
 Anzahl der Seiten
 133
 Publikationsdatum
 2020
 Publikationsstatus
 Veröffentlicht
 Elektronische Version(en)

https://doi.org/10.15488/10085 (Zugang:
Offen)