https://doi.org/10.1140/epjc/s10052-024-13332-1
Regular Article - Theoretical Physics
Tunnelling amplitudes through localised external potentials from Feynman diagram summation
1
Department of Fundamental and Theoretical Physics, The Australian National University, Canberra, Australia
2
Department of Nuclear Physics and Accelerator Applications, The Australian National University, Canberra, Australia
a
rosemary.zielinski@anu.edu.au
Received:
21
May
2024
Accepted:
4
September
2024
Published online:
30
September
2024
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.
© The Author(s) 2024
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