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Quantum Electrodynamics at Small Distances

Gell-Mann, M. and Low, F. E. (1954) Quantum Electrodynamics at Small Distances. Physical Review, 95 (5). pp. 1300-1312. ISSN 0031-899X. doi:10.1103/PhysRev.95.1300.

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The renormalized propagation functions DFC and SFC for photons and electrons, respectively, are investigated for momenta much greater than the mass of the electron. It is found that in this region the individual terms of the perturbation series to all orders in the coupling constant take on very simple asymptotic forms. An attempt to sum the entire series is only partially successful. It is found that the series satisfy certain functional equations by virtue of the renormalizability of the theory. If photon self-energy parts are omitted from the series, so that D_(FC)=D_F, then S_(FC) has the asymptotic form A[p^2m^2]^n[iγ⋅p]^(−1), where A=A(e_1^2) and n=n(e_1^2). When all diagrams are included, less specific results are found. One conclusion is that the shape of the charge distribution surrounding a test charge in the vacuum does not, at small distances, depend on the coupling constant except through a scale factor. The behavior of the propagation functions for large momenta is related to the magnitude of the renormalization constants in the theory. Thus it is shown that the unrenormalized coupling constant e_0^2/4πℏc, which appears in perturbation theory as a power series in the renormalized coupling constant e_1^2/4πℏc with divergent coefficients, may behave in either of two ways: (a) It may really be infinite as perturbation theory indicates; (b) It may be a finite number independent of e_1^2/4πℏc.

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Additional Information:© 1953 American Physical Society. Received 1 April 1954. This work was supported by grants from the U. S. Office of Naval Research and the U. S. Atomic Energy Commission. Now at Department of Physics and Institute for Nuclear Studies, University of Chicago.
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Office of Naval Research (ONR)UNSPECIFIED
Atomic Energy CommissionUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20150924-084900714
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Official Citation:Quantum Electrodynamics at Small Distances M. Gell-Mann and F. E. Low Phys. Rev. 95, 1300 – Published 1 September 1954
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60469
Deposited By: Ruth Sustaita
Deposited On:24 Sep 2015 20:56
Last Modified:10 Nov 2021 22:34

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