Vacuum energy in the bag model
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.
KeywordsSurface Tension Volume Energy Vacuum Energy Similar Instability High Frequency Effect
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