Vacuum energy in the bag model

  • P. Candelas
Quantum Field Theory in Curved Space-Time
Part of the Lecture Notes in Physics book series (LNP, volume 176)


The vacuum energy of the Yang-Mills field is examined for the conditions of the bag model. The dominance of high frequency effects results in a vacuum energy that decomposes naturally into a volume energy, a surface energy and higher shape energies. These quantities are identified with the parameters of the bag model. The imposition of confining boundary conditions for all frequencies is shown to be inconsistent since this would result in the bag constant and certain of the shape tensions being infinite. The manner in which the boundary conditions should be relaxed at high frequency is discussed. The most naive procedure for relaxing the boundary conditions, which is to apply confining conditions only on modes of frequency less than some cutoff frequency, results in a negative bag constant and surface tension and would render the vacuum unstable against the spontaneous breaking of Poincaré invariance. Consideration of the manner by which the interacting electromagnetic field avoids a similar instability suggests that a more realistic way to relax the boundary conditions on the bag surface is to endow the vacuum exterior to the bag with a frequency dependent dielectric constant and magnetic permeability.


Surface Tension Volume Energy Vacuum Energy Similar Instability High Frequency Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [1]
    J. Kuti and P. Hasenfratz, Phys. Rep. 40, 45 (1978).Google Scholar
  2. [2]
    J.F. Donoghue and K. Johnson, Phys. Rev. D21, 1975 (1980).Google Scholar
  3. [3]
    K. Johnson, in Particles and Fields — 1979 (APS/DPF Montreal). B. Margolis and D.G. Stairs, eds., AIP, New York, 1980.Google Scholar
  4. [4]
    T.H. Boyer, Phys. Rev. 174, 1764 (1968).CrossRefGoogle Scholar
  5. [5]
    K.A. Milton, L.L. DeRaad, Jr., and J. Schwinger, Ann. Phys. (N.Y.) 115, 388 (1978).Google Scholar
  6. [6]
    P. Candelas, “Vacuum energy in the presence of dielectric and conducting surfaces.” To appear in Ann. Phys. (N.Y.).Google Scholar
  7. [7]
    P. Candelas, “Vacuum energy in the bag model,” Center for Theoretical Physics preprint.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • P. Candelas
    • 1
  1. 1.Center for Theoretical PhysicsThe University of Texas at AustinAustinUSA

Personalised recommendations