Fermionic duality

Abstract

Duality transformations play a very important role in theoretical physics. In this paper I propose new duality transformations for fermionic theories. They map the strong coupling regime of one theory to the weak coupling regime of another theory. These transformations are based on the functional integral representation of the fermionic theories in terms of Grassmann variables and rely heavily on the properties of Grassmann variables. Potential applications include the study of the strong coupling phase of the two dimensional Hubbard model.