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arXiv · 2512.16667

Field Quantisations in Schwarzschild Spacetime: Theory versus Low-Energy Experiments

Viacheslav A. Emelyanov
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Abstract

Non-relativistic quantum particles in the Earth's gravitational field are successfully described by the Schr\"{o}dinger equation with Newton's gravitational potential. Particularly, quantum mechanics is in agreement with such experiments as free fall and quantum interference induced by gravity. However, quantum mechanics is a low-energy approximation to quantum field theory. The latter is successful by the description of high-energy experiments. Gravity is embedded in quantum field theory through the general-covariance principle. This framework is known in the literature as quantum field theory in curved spacetime, where the concept of a quantum particle is, though, ambiguous. In this article, we study in this framework how a Hawking particle moves in the far-horizon region of Schwarzschild spacetime by computing its propagator. We find this propagator differs from that which follows from the path-integral formalism -- the formalism which adequately describes both free fall and quantum interference induced by gravity.

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Viacheslav A. Emelyanov. 2025-12-18. Field Quantisations in Schwarzschild Spacetime: Theory versus Low-Energy Experiments. https://doi.org/10.1103/s94y-zx6m

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