SPATIAL DYNAMICS IN THE KAZAKOV-MIGDAL MODEL

The spatially inhomogeneous large N solutions to the Kazakov-Migdal model are analyzed. A set of nonlinear differential equations is derived in the continuum limit. In the one dimensional case these equations have a natural interpretation in terms of the dynamics of a Fermi gas. In the multidimensional case we have found two possibilities to take the continuum limit. One of them leads to a one-component phi3 theory, while the other seems to be inconsistent because of its instability related to the collapse of eigenvalues of the matrix scalar field.