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arXiv · 2405.11779

Tunnelling amplitudes through localised external potentials from Feynman diagram summation

Rosemary Zielinski·Cedric Simenel·Patrick McGlynn
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Abstract

Currently there is no general theory of quantum tunnelling of a particle through a potential barrier which is compatible with QFT. We present a complete calculation of tunnelling amplitudes for a scalar field for some simple potentials using quantum field-theoretic methods. Using the perturbative S-matrix formalism, starting with the Klein-Gordon Lagrangian, we show that an infinite summation of Feynman diagrams can recover tunnelling amplitudes consistent with relativistic quantum mechanics. While this work does not include many-particle effects arising from a fully quantised QFT, it is necessary to investigate QFT corrections to tunnelling amplitudes.

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Rosemary Zielinski, Cedric Simenel, Patrick McGlynn. 2024-05-20. Tunnelling amplitudes through localised external potentials from Feynman diagram summation. https://doi.org/10.1140/epjc%2Fs10052-024-13332-1

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