Structure and Stability of a Weakly Interacting Instanton and Anti-Instanton System Under External Fields. II

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The Euclidean vacuum in quantum chromodynamics is studied by the statistical mechanics method. The magnetic permeability shows an abrupt change at a certain value of the external color electric field, when the dipolar interaction between instantons and antiinstantons is partly considered through the local effective gauge field in determining the mean dipole moment of instantons. The equilibrium states in this transition region are unstable, while all other equilibrium states are stable. The abrupt change in the magnetic permeability continues to hold even When the energy of dipolar interactions with the large cutoff length is introduced explicitly into the free energy. But, in this case, we have a new branch of unstable equilibrium configurations separated from the branch containing stable and unstable (transition region) states. When the cutoff length becomes small, such a structure in the magnetic permeability disappears and further, we have two connected branches of equilibrium configurations with high (unstable) or low (stable) instanton densities, similar to those for the dipolar interaction with a particular instanton-size-dependent cutoff considered previously.
理論物理学刊行会の論文
1980-11-25