We study the non-relativistic limit of quantum fields for an inertial and a non-inertial observer. We show that non-relativistic particle states appear as a superposition of relativistic and non-relativistic particles in different frames. Hence, the non-relativistic limit is frame-dependent. We detail this result when the non-inertial observer has uniform constant acceleration. Only for low accelerations, the accelerated observer agrees with the inertial frame about the non-relativistic nature of particles locally. In such a quasi-inertial regime, both observers agree about the number of particles describing quantum field states. The same does not occur when the acceleration is arbitrarily large (e.g., the Unruh effect). We furthermore prove that wave functions of particles in the inertial and the quasi-inertial frame are identical up to the coordinate transformation relating the two frames.

Frame dependence of the nonrelativistic limit of quantum fields / Falcone, Riccardo; Conti, Claudio. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 107:8(2023), pp. 1-15. [10.1103/PhysRevD.107.085016]

Frame dependence of the nonrelativistic limit of quantum fields

Riccardo Falcone
;
Claudio Conti
2023

Abstract

We study the non-relativistic limit of quantum fields for an inertial and a non-inertial observer. We show that non-relativistic particle states appear as a superposition of relativistic and non-relativistic particles in different frames. Hence, the non-relativistic limit is frame-dependent. We detail this result when the non-inertial observer has uniform constant acceleration. Only for low accelerations, the accelerated observer agrees with the inertial frame about the non-relativistic nature of particles locally. In such a quasi-inertial regime, both observers agree about the number of particles describing quantum field states. The same does not occur when the acceleration is arbitrarily large (e.g., the Unruh effect). We furthermore prove that wave functions of particles in the inertial and the quasi-inertial frame are identical up to the coordinate transformation relating the two frames.
2023
unruh effect; quantum field theory in curved spacetime; rindler; accelerated; frame dependent; nonrelativistic limit
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Frame dependence of the nonrelativistic limit of quantum fields / Falcone, Riccardo; Conti, Claudio. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 107:8(2023), pp. 1-15. [10.1103/PhysRevD.107.085016]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1693931
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