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Spontaneous Symmetry Breakdown and the μ−e−γ Interaction

Arnowitt, R. and Deser, S. (1965) Spontaneous Symmetry Breakdown and the μ−e−γ Interaction. Physical Review, 138 (3B). B712-B723. ISSN 0031-899X. doi:10.1103/physrev.138.b712.

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Spontaneous breakdowns of symmetries have been examined for a system of two charged fields of zero bare mass (the "muon" and "electron" fields) interacting minimally with the electromagnetic field. Upon arranging the two fields into an "isotopic" doublet, the Lagrangian is seen to posses SU(2)symmetry. Three possibilities are available: (a) no spontaneous breakdown of the SU(2) symmetry is allowed and the muon-electron system remains a degenerate doublet; (b) a partial breakdown occurs in which a mass splitting develops but the heavier muon remains stable; (c) a complete breakdown occurs in which the muon decays into an electron plus a photon. Using the high-energy scheme of Baker, Johnson, and Willey, approximate solutions for the one-fermion Green's function and vertex function are examined. (The approximation scheme has the advantage that no ad hoc cutoffs need be invoked.) The solutions obtained permit case (b) to occur but not case (c), provided improper Lorentz invariance is imposed. It is shown, at least for the one-fermion Green's function, that no solutions breaking P, C, or T invariance can arise.

Item Type:Article
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Deser, S.0000-0001-9285-9434
Additional Information:© 1965 American Physical Society. (Received 28 December 1964) Supported in part by the National Science Foundation. Supported in part by U. S. Air Force Office of Scientific Research.
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Issue or Number:3B
Record Number:CaltechAUTHORS:20180724-143009755
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88206
Deposited By: George Porter
Deposited On:24 Jul 2018 22:20
Last Modified:16 Nov 2021 00:24

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