Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes
Abstract In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitabl...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2020)018 |
| _version_ | 1818429037348913152 |
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| author | N. Ahmadiniaz V.M. Banda Guzmán F. Bastianelli O. Corradini J.P. Edwards C. Schubert |
| author_facet | N. Ahmadiniaz V.M. Banda Guzmán F. Bastianelli O. Corradini J.P. Edwards C. Schubert |
| author_sort | N. Ahmadiniaz |
| collection | DOAJ |
| description | Abstract In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N -photon kernel,” where off-shell this kernel appears also in “subleading” terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter. |
| first_indexed | 2024-12-14T15:11:09Z |
| format | Article |
| id | doaj.art-16d81c7a5b144f48b57dc9daf40b55cb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T15:11:09Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-16d81c7a5b144f48b57dc9daf40b55cb2022-12-21T22:56:33ZengSpringerOpenJournal of High Energy Physics1029-84792020-08-012020814910.1007/JHEP08(2020)018Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudesN. Ahmadiniaz0V.M. Banda Guzmán1F. Bastianelli2O. Corradini3J.P. Edwards4C. Schubert5Helmholtz-Zentrum Dresden-RossendorfInstituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de HidalgoDipartimento di Fisica ed Astronomia, Università di BolognaINFN — Sezione di BolognaInstituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de HidalgoInstituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de HidalgoAbstract In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons, in terms of the “N -photon kernel,” where off-shell this kernel appears also in “subleading” terms involving only N − 1 of the N photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the N = 2 case for a recalculation of the one-loop fermion self energy, in D dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation by choosing an unusual momentum-dependent gauge parameter.http://link.springer.com/article/10.1007/JHEP08(2020)018Scattering AmplitudesGauge SymmetrySuperspaces |
| spellingShingle | N. Ahmadiniaz V.M. Banda Guzmán F. Bastianelli O. Corradini J.P. Edwards C. Schubert Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes Journal of High Energy Physics Scattering Amplitudes Gauge Symmetry Superspaces |
| title | Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes |
| title_full | Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes |
| title_fullStr | Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes |
| title_full_unstemmed | Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes |
| title_short | Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes |
| title_sort | worldline master formulas for the dressed electron propagator part i off shell amplitudes |
| topic | Scattering Amplitudes Gauge Symmetry Superspaces |
| url | http://link.springer.com/article/10.1007/JHEP08(2020)018 |
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