Fermionic duality

TL;DR

This paper introduces new duality transformations for fermionic theories that relate strong and weak coupling regimes, leveraging Grassmann variables, with potential applications in condensed matter physics.

Contribution

It proposes novel duality transformations for fermionic theories based on Grassmann variables, enabling analysis of strong coupling regimes.

Findings

Duality transformations map strong to weak coupling regimes.

Potential application to the 2D Hubbard model's strong coupling phase.

Framework relies on Grassmann variable properties.

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.