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In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], Lammerzahl [2] and Giulini and Grosardt [3] to arbitrary order… Click to show full abstract
In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], Lammerzahl [2] and Giulini and Grosardt [3] to arbitrary order in $c^{-1}$, leading to Schrodinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following Wajima et al. [4]. Furthermore, using a more operator-algebraic approach, the Klein--Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any `non-relativistic' expansion.
Journal Title: Classical and Quantum Gravity
Year Published: 2019
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