Point-particle effective field theory III: relativistic fermions and the Dirac equation
Abstract We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with whi...
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doaj-8a7be046367647dfa66b4aff9ac5b0a52020-11-24T23:28:50ZengSpringerOpenJournal of High Energy Physics1029-84792017-09-012017915310.1007/JHEP09(2017)007Point-particle effective field theory III: relativistic fermions and the Dirac equationC. P. Burgess0Peter Hayman1Markus Rummel2László Zalavári3Department of Physics & Astronomy, McMaster UniversityDepartment of Physics & Astronomy, McMaster UniversityDepartment of Physics & Astronomy, McMaster UniversityDepartment of Physics & Astronomy, McMaster UniversityAbstract We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.http://link.springer.com/article/10.1007/JHEP09(2017)007Effective Field TheoriesNonperturbative EffectsRenormalization Group |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
C. P. Burgess Peter Hayman Markus Rummel László Zalavári |
spellingShingle |
C. P. Burgess Peter Hayman Markus Rummel László Zalavári Point-particle effective field theory III: relativistic fermions and the Dirac equation Journal of High Energy Physics Effective Field Theories Nonperturbative Effects Renormalization Group |
author_facet |
C. P. Burgess Peter Hayman Markus Rummel László Zalavári |
author_sort |
C. P. Burgess |
title |
Point-particle effective field theory III: relativistic fermions and the Dirac equation |
title_short |
Point-particle effective field theory III: relativistic fermions and the Dirac equation |
title_full |
Point-particle effective field theory III: relativistic fermions and the Dirac equation |
title_fullStr |
Point-particle effective field theory III: relativistic fermions and the Dirac equation |
title_full_unstemmed |
Point-particle effective field theory III: relativistic fermions and the Dirac equation |
title_sort |
point-particle effective field theory iii: relativistic fermions and the dirac equation |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2017-09-01 |
description |
Abstract We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei. |
topic |
Effective Field Theories Nonperturbative Effects Renormalization Group |
url |
http://link.springer.com/article/10.1007/JHEP09(2017)007 |
work_keys_str_mv |
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