Tunnelling amplitudes through localised external potentials from Feynman diagram summation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929530782875648 |
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| author | Zielinski, Rosemary Simenel, Cedric McGlynn, Patrick |
| author_facet | Zielinski, Rosemary Simenel, Cedric McGlynn, Patrick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tunnelling amplitudes through localised external potentials from Feynman diagram summation Zielinski, Rosemary Simenel, Cedric McGlynn, Patrick High Energy Physics - Theory Nuclear Theory 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. |
| title | Tunnelling amplitudes through localised external potentials from Feynman diagram summation |
| topic | High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2405.11779 |