We show that spacetime evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a spacetime dependence of a matrix element of fermionic systems related to the orthogonality catastrophe or boundary states with the τ-function of the modified KP-hierarchy. The established relation allows us to apply the apparatus of soliton theory to the study of nonlinear aspects of quantum dynamics. We also describe a bosonization in momentum space-a representation of a fermion operator by a Bose field in the presence of a boundary state.
|Journal of Physics A: Mathematical and Theoretical
|Published - 23 Feb 2007