Classical adiabatic holonomy in field theory

In this paper we develop the notion of adiabatic holonomy in classical fermionic field theory and apply it to chiral gauge theory. In chiral gauge theory the classical adiabatic holonomy leads to a deformation of the Poisson algebra of translation generators in the space of gauge fields and to an additional term in the Poisson brackets among gauge-transformation generators. We study all this in detail in a (1+1)-dimensional model.