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Equal-Time Commutators and Electromagnetic Mass Splittings

Boulware, David G. and Deser, S. (1968) Equal-Time Commutators and Electromagnetic Mass Splittings. Physical Review, 175 (5). pp. 1912-1933. ISSN 0031-899X. https://resolver.caltech.edu/CaltechAUTHORS:20170317-143109687

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Abstract

The relation between electromagnetic mass shifts (or splittings) to order α and equal-time commutators is analyzed. If the invariants in the forward spin-averaged Compton amplitude go as k^(−2) for k^2 → ∞, it is possible to relate the quadratic and logarithmic divergences in δm^2 to certain Lorentz scalars formed from the commutators. These results are illustrated by models with currents bilinear or linear in canonical fields. The Jost-Lehmann representation is then used to analyze more general behavior. It is shown that the spectral function may generate a higher-rank tensor character of the amplitude than that expected from its kinematic factors. The relation is then more complicated even if the commutators still exist. Finally, detailed criteria for the existence of equal-time commutators are developed.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRev.175.1912DOIArticle
http://journals.aps.org/pr/abstract/10.1103/PhysRev.175.1912PublisherArticle
ORCID:
AuthorORCID
Deser, S.0000-0001-9285-9434
Additional Information:© 1968 American Physical Society. (Received 17 June 1968) We wish to thank the 1967 Summer Institute of the Niels Bohr Institute for hospitality while this work was begun. One of us (D.G.B.) also thanks Brookhaven National Laboratory and Professor Abdus Salam and the International Atomic Energy Association for hospitality at the International Centre of Theoretical Physics, Trieste, while the work was completed. Work supported by U. S. Atomic Energy Commission under Grant No. RCO-1388B. Work supported by U. S. Air Force Office of Aerospace Research under Office of Scientific Research Grant No. AF 368-67.
Funders:
Funding AgencyGrant Number
Atomic Energy CommissionRCO-1388B
Air Force Office of Scientific Research (AFOSR)AF 368-67
Issue or Number:5
Record Number:CaltechAUTHORS:20170317-143109687
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170317-143109687
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75212
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Mar 2017 22:32
Last Modified:03 Oct 2019 16:47

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