We show that the Euclidean vacuum in quantum chromodynamics (QCD) can be regarded as a four-dimensional ensemble of permanent color magnetic dipoles (instantons and meron pairs), with a positive paramagnetic susceptibility. Standard techniques are used to discuss the interactions of this medium for moderate densities. In the presence of color fields (due to quarks), large scale instantons (and other fluctuations) are suppressed, the density is low, and the system is easily treated. Below a critical field strength, this dilute phase is unstable and a first-order phase transition occurs to a dense phase consisting of closely packed instantons and merons, and possibly other things. In this dense phase, we believe that the permeability is infinite (perfect paramagnetism) and thus the normal QCD vacuum cannot tolerate color fields. This leads to a strikingly simple baglike picture of hadrons, as consisting of quarks confined to a region of space-time which is in a very dilute (abnormal) vacuum phase, in equilibrium with the dense vacuum (normal) phase outside the bag. The quarks are confined to the region of dilute phase where their dynamics are simple; and, as we show, they are shielded from the large-scale fluctuations outside the bag. We present a derivation of the static bag for heavy quarks and an estimate (to within a factor of two) of the bag constant. We further discuss some features of the resulting bag model including chiral-symmetry breaking and surface effects.

• Received 10 August 1978

DOI:https://doi.org/10.1103/PhysRevD.19.1826