Vacuum Bubble Instantons

  • P. H. Frampton
Part of the Studies in the Natural Sciences book series (SNS, volume 13)


In these remarks, we discuss the existence of certain instanton solutions occurring in both non-gauge and gauge field theories. They are not associated with the mapping of a non-Abelian gauge group on S3, have no conserved topological charge and are hence unstable. They provide probably the principal decay mechanism of an unstable vacuum and standard instanton methods2–4 can be exploited to estimate such a vacuum decay lifetime.


Topological Charge Gauge Field Theory Metastable Vacuum Physical Vacuum Instanton Solution 
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  1. 1.
    P. H. Frampton, Phys. Rev. Letters 37, 1378 (1976). This calculation has recently been justified by S. Coleman (Harvard University preprint).ADSCrossRefGoogle Scholar
  2. 2.
    A. A. Belavin et al., Phys. Letters 59B, 85 (1975).MathSciNetADSGoogle Scholar
  3. 3.
    G. ’t Hooft, Phys. Rev. Letters 37, 8 (1976).ADSCrossRefGoogle Scholar
  4. 4.
    R. Jackiw and C. Rebbi, Phys. Rev. Letters 37, 172 (1976).ADSCrossRefGoogle Scholar
  5. 5.
    Since the bubble is created with Pμ =0, its momentum is the same in all Lorentz frames; to put the same statement differently, the bubble expanding at the speed of light appears spherical to all observers. Thus no momentum can be associated with the bubble and no (divergent) phase space integral is necessary here. This point was first made clear to me in the discussion following my seminar at SLAC, November 1976.Google Scholar
  6. 6.
    It is here assumed that non-spherical instantons, necessarily having larger classical action, may be safely neglected.Google Scholar
  7. 7.
    C. Callan and S. Coleman, preprint in preparation.Google Scholar
  8. 8.
    D. Gross, these proceedings.Google Scholar
  9. 9.
    A. Salam, International Symposium “Five Decades of Weak Interactions,” City College N.Y. January 1977. Salam suggests that because of the difficulty in establishing confinement for quarks exchanging spin-one gluons unification with gravity, in particular spin-two gluons, might be necessary to ensure confinement through a black-hole-type mechanism.Google Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • P. H. Frampton
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaLos AngelesUSA

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