SciPost Submission Page
A coupling prescription for post-Newtonian corrections in Quantum Mechanics
by Jelle Hartong, Emil Have, Niels A. Obers, Igor Pikovski
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users): | Emil Have · Niels Obers |
Submission information | |
---|---|
Preprint Link: | scipost_202402_00005v2 (pdf) |
Date accepted: | 2024-03-11 |
Date submitted: | 2024-03-05 19:30 |
Submitted by: | Have, Emil |
Submitted to: | SciPost Physics |
Ontological classification | |
---|---|
Academic field: | Physics |
Specialties: |
|
Approach: | Theoretical |
Abstract
The interplay between quantum theory and general relativity remains one of the main challenges of modern physics. A renewed interest in the low-energy limit is driven by the prospect of new experiments that could probe this interface. Here we develop a covariant framework for expressing post-Newtonian corrections to Schr\"odinger's equation on arbitrary gravitational backgrounds based on a $1/c^2$ expansion of Lorentzian geometry, where $c$ is the speed of light. Our framework provides a generic coupling prescription of quantum systems to gravity that is valid in the intermediate regime between Newtonian gravity and General Relativity, and that retains the focus on geometry. At each order in $1/c^2$ this produces a nonrelativistic geometry to which quantum systems at that order couple. By considering the gauge symmetries of both the nonrelativistic geometries and the $1/c^2$ expansion of the complex Klein-Gordon field, we devise a prescription that allows us to derive the Schr\"odinger equation and its post-Newtonian corrections on a gravitational background order-by-order in $1/c^2$. We also demonstrate that these results can be obtained from a $1/c^2$ expansion of the complex Klein-Gordon Lagrangian. We illustrate our methods by performing the $1/c^2$ expansion of the Kerr metric up to $\mathcal{O}(c^{-2})$, which leads to a special case of the Hartle-Thorne metric. The associated Schr\"odinger equation captures novel and potentially measurable effects.
Author comments upon resubmission
List of changes
See the response, which is attached as a reply to the second referee.
Published as SciPost Phys. 16, 088 (2024)
Reports on this Submission
Report #1 by Philip Schwartz (Referee 1) on 2024-3-7 (Invited Report)
Report
I thank the authors for their work in addressing my comments. I recommend publication of the revised manuscript in its current form.