A general method is presented for evaluating, in a model-independent way, the soft virtual photon radiative corrections to an arbitrary hadronic process. It is shown that all the results concerning infrared divergences obtained within the theory of quantum electrodynamics of the electron-photon system are, in fact, exact in strong interactions. The problem of radiative corrections to low-energy theorems is the primary concern of this investigation. The threshold contributions of intermediate soft photon states are non-analytic in the photon-frequency (ω). While the procedure is general enough to permit, in principle, the calculation of the leading terms (as ω→0) of these radiative corrections to all orders in e, in this paper only the leading e² radiative corrections are computed explicitly: they are of the order Inω for the bremsstrahlung (as first noted by Soloviev); of the order ωlnω for pion-photo-production. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the O(ω⁰) bremsstrahlung and O(ω) pion-photoproduction amplitudes. The e⁴ Compton amplitude O(ω²lnω) is computed and shown to be independent of the target spin. A review of the usual low energy theorems, which have been proven to the lowest order in e, also will be presented.
","abstract_html":"<p>A general method is presented for evaluating, in a model-independent way, the soft virtual photon radiative corrections to an arbitrary hadronic process. It is shown that all the results concerning infrared divergences obtained within the theory of quantum electrodynamics of the electron-photon system are, in fact, exact in strong interactions. The problem of radiative corrections to low-energy theorems is the primary concern of this investigation. The threshold contributions of intermediate soft photon states are non-analytic in the photon-frequency (ω). While the procedure is general enough to permit, in principle, the calculation of the leading terms (as ω→0) of these radiative corrections to all orders in e, in this paper only the leading e² radiative corrections are computed explicitly: they are of the order Inω for the bremsstrahlung (as first noted by Soloviev); of the order ωlnω for pion-photo-production. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the O(ω⁰) bremsstrahlung and O(ω) pion-photoproduction amplitudes. The e⁴ Compton amplitude O(ω²lnω) is computed and shown to be independent of the target spin. A review of the usual low energy theorems, which have been proven to the lowest order in e, also will be presented.</p>","abstract_has_math":false,"creators":["Cheng, Ta-Pei"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Abraham Pais"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1969,"date_issued":"1969-01-01T08:00:00Z","date_published":"1969-01-01T08:00:00Z","updated_at":"2026-07-24T04:11:55Z","subjects":["soft photon corrections","radiative corrections","low-energy theorems","infrared divergence","bremsstrahlung","pion photoproduction","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/558","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Abraham Pais"]},{"key":"dc:creator","label":"Author","values":["Cheng, Ta-Pei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["soft photon corrections","radiative corrections","low-energy theorems","infrared divergence","bremsstrahlung","pion photoproduction","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/558"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A general method is presented for evaluating, in a model-independent way, the soft virtual photon radiative corrections to an arbitrary hadronic process. It is shown that all the results concerning infrared divergences obtained within the theory of quantum electrodynamics of the electron-photon system are, in fact, exact in strong interactions. The problem of radiative corrections to low-energy theorems is the primary concern of this investigation. The threshold contributions of intermediate soft photon states are non-analytic in the photon-frequency (ω). While the procedure is general enough to permit, in principle, the calculation of the leading terms (as ω→0) of these radiative corrections to all orders in e, in this paper only the leading e² radiative corrections are computed explicitly: they are of the order Inω for the bremsstrahlung (as first noted by Soloviev); of the order ωlnω for pion-photo-production. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the O(ω⁰) bremsstrahlung and O(ω) pion-photoproduction amplitudes. The e⁴ Compton amplitude O(ω²lnω) is computed and shown to be independent of the target spin. A review of the usual low energy theorems, which have been proven to the lowest order in e, also will be presented.
"]},{"key":"dc:title","label":"Title","values":["Radiative Corrections to Low Energy Theorems"]}]}],"canonical_facts":{"dc:contributor":["Abraham Pais"],"dc:creator":["Cheng, Ta-Pei"],"dc:description.abstract":["A general method is presented for evaluating, in a model-independent way, the soft virtual photon radiative corrections to an arbitrary hadronic process. It is shown that all the results concerning infrared divergences obtained within the theory of quantum electrodynamics of the electron-photon system are, in fact, exact in strong interactions. The problem of radiative corrections to low-energy theorems is the primary concern of this investigation. The threshold contributions of intermediate soft photon states are non-analytic in the photon-frequency (ω). While the procedure is general enough to permit, in principle, the calculation of the leading terms (as ω→0) of these radiative corrections to all orders in e, in this paper only the leading e² radiative corrections are computed explicitly: they are of the order Inω for the bremsstrahlung (as first noted by Soloviev); of the order ωlnω for pion-photo-production. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the O(ω⁰) bremsstrahlung and O(ω) pion-photoproduction amplitudes. The e⁴ Compton amplitude O(ω²lnω) is computed and shown to be independent of the target spin. A review of the usual low energy theorems, which have been proven to the lowest order in e, also will be presented.
"],"dc:identifier":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/558"],"dc:subject":["soft photon corrections","radiative corrections","low-energy theorems","infrared divergence","bremsstrahlung","pion photoproduction","Physical Sciences and Mathematics"],"dc:title":["Radiative Corrections to Low Energy Theorems"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:11:55Z"}