dorsal/arxiv
View SchemaField transformations and simple models illustrating the impossibility of measuring off-shell effects
| Authors | H. W. Fearing, S. Scherer |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9909076 |
| URL | https://arxiv.org/abs/nucl-th/9909076 |
| DOI | 10.1103/PhysRevC.62.034003 |
| Journal | Phys.Rev. C62 (2000) 034003 |
Abstract
In the context of simple models illustrating field transformations in Lagrangian field theories we discuss the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung, Compton scattering, and related processes. To that end we introduce a simple phenomenological Lagrangian describing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon amplitude as well as the photon-nucleon vertex. As a result we obtain a class of equivalent Lagrangians, generating identical S-matrix elements, of which the original Lagrangian is but one representative. We make use of this property in order to show that what appears as an off-shell effect in an S-matrix element for one Lagrangian may originate in a contact term from an equivalent Lagrangian. By explicit calculation we demonstrate for the case of nucleon-nucleon bremsstrahlung as well as nucleon Compton scattering the equivalence of observables from which we conclude that off-shell effects cannot in any unambiguous way be extracted from an S-matrix element. Finally, we also discuss some implications of introducing off-shell effects on a phenomenological basis, resulting from the requirement that the description of one process be consistent with that of other processes described by the same Lagrangian.
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"abstract": "In the context of simple models illustrating field transformations in\nLagrangian field theories we discuss the impossibility of measuring off-shell\neffects in nucleon-nucleon bremsstrahlung, Compton scattering, and related\nprocesses. To that end we introduce a simple phenomenological Lagrangian\ndescribing nucleon-nucleon bremsstrahlung and perform an appropriate change of\nvariables leading to different off-shell behavior in the nucleon-nucleon\namplitude as well as the photon-nucleon vertex. As a result we obtain a class\nof equivalent Lagrangians, generating identical S-matrix elements, of which the\noriginal Lagrangian is but one representative. We make use of this property in\norder to show that what appears as an off-shell effect in an S-matrix element\nfor one Lagrangian may originate in a contact term from an equivalent\nLagrangian. By explicit calculation we demonstrate for the case of\nnucleon-nucleon bremsstrahlung as well as nucleon Compton scattering the\nequivalence of observables from which we conclude that off-shell effects cannot\nin any unambiguous way be extracted from an S-matrix element. Finally, we also\ndiscuss some implications of introducing off-shell effects on a\nphenomenological basis, resulting from the requirement that the description of\none process be consistent with that of other processes described by the same\nLagrangian.",
"arxiv_id": "nucl-th/9909076",
"authors": [
"H. W. Fearing",
"S. Scherer"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.62.034003",
"journal_ref": "Phys.Rev. C62 (2000) 034003",
"title": "Field transformations and simple models illustrating the impossibility of measuring off-shell effects",
"url": "https://arxiv.org/abs/nucl-th/9909076"
},
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