Lettere al Nuovo Cimento (1971-1985)

, Volume 33, Issue 1, pp 45–46 | Cite as

Permutation symmetry and leptonic mass

  • G. Rosen


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  6. (6).
    Clearly, the similarity-equivalent matrices for e↔τ and μ↔τ also have the secular determinant (4) and likewise yield formula (5). In the case of the infinite-order mass-renormalization seriec form (of flavorf), the permutation, symmetry of interest is that which transposes the other two leptonic field operators (and thus relabels their associated internal lines), because the external lepton lines are fixed in all relevant self-energy and counterterm graphs form. The quatity |Δ(f)|2 appears in (5) as a measure of permutation-symmetry breakdown, with symmetrical eigenstates ofP having eigenvalue +1 and Δ(1)=0. While further detailed analysis is required to show how (5) arises as a self-consistency condition on the mass-renormalization series form, the appearance of the secular determinant is suggestive of a Feenburg perturbation theory representation, (see:H. Feshbach:Phys. Rev.,74, 1548 (1948).Google Scholar
  7. (7).
    Since (f 4+1)(f−1)4=32 forf=−1 andN=4, thef=−1, flavor assignment requires a charged lepton at 3.362 GeV, which is ruled out by experiment. Thus, one can postulate thatf is a nonnegative integer.Google Scholar

Copyright information

© Società Italiana di Fisica 1982

Authors and Affiliations

  • G. Rosen
    • 1
  1. 1.Department of PhysicsDrexel UniversityPhiladelphia

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