Details
| Original language | English |
|---|---|
| Article number | 095016 |
| Journal | Classical and Quantum Gravity |
| Volume | 36 |
| Issue number | 9 |
| Early online date | 12 Apr 2019 |
| Publication status | Published - 9 May 2019 |
Abstract
In this paper we extend the WKB-like 'non-relativistic' expansion of the minimally coupled Klein-Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067-76; Lammerzahl 1995 Phys. Lett. A 203 12-7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c -1, leading to Schrödinger 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 1997 Phys. Rev. D 55 1964-70). 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.
Keywords
- formal WKB expansion, Klein-Gordon equation, non-relativistic expansion, post-Newtonian expansion, quantum matter in gravity
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Classical and Quantum Gravity, Vol. 36, No. 9, 095016, 09.05.2019.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Post-Newtonian corrections to Schrödinger equations in gravitational fields
AU - Schwartz, Philip K.
AU - Giulini, Domenico
N1 - Funding information: The authors would like to thank two anonymous referees for valuable comments on the manuscript. This work was supported by the Deutsche Forschungsgemeinschaft through the Collaborative Research Centre 1227 (DQ-mat), project B08.
PY - 2019/5/9
Y1 - 2019/5/9
N2 - In this paper we extend the WKB-like 'non-relativistic' expansion of the minimally coupled Klein-Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067-76; Lammerzahl 1995 Phys. Lett. A 203 12-7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c -1, leading to Schrödinger 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 1997 Phys. Rev. D 55 1964-70). 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.
AB - In this paper we extend the WKB-like 'non-relativistic' expansion of the minimally coupled Klein-Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067-76; Lammerzahl 1995 Phys. Lett. A 203 12-7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c -1, leading to Schrödinger 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 1997 Phys. Rev. D 55 1964-70). 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.
KW - formal WKB expansion
KW - Klein-Gordon equation
KW - non-relativistic expansion
KW - post-Newtonian expansion
KW - quantum matter in gravity
UR - http://www.scopus.com/inward/record.url?scp=85067365882&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1812.05181
DO - 10.48550/arXiv.1812.05181
M3 - Article
AN - SCOPUS:85067365882
VL - 36
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 9
M1 - 095016
ER -