Exact Euler-Heisenberg Effective Action for Chiral Fermions in Some Special External Fields

Abstract

The quantity of central importance in quantum field theory is just not the action of its classical counterpart but the partition function that contains it and also the path measures. As a consequence even if the action part is trivial, i.e., it is equivalent to a free theory by redefining the phases of the complex fields, the quantum theory may not still be trivial. The path measures may acquire a nontrivial Jacobian because of this redefinition of the variables. Analogous thing was the approach of Fujikawa [1] to study the axial anomaly, except that in those cases only the infinitesimal variation (Ward identities) of the effective actions are calculable. The contention of the present talk is that for the classically trivial theories involving chiral fermions in any even space time dimensions the complete effective actions can be exactly evaluated. The techniques involved are well known [2] but the final results are interesting. Below is a short prescription.