Electrodynamics in a Background Chiral Field

Abstract

We consider the one loop effective action in four dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass $m$ of the spinor vanishes. If $m$ does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.

9 pages, references added, minor corrections, typos fixed, accepted in Mod. Phys. Lett. A

References in corpus (2)

• Two-Loop Vacuum Diagrams in Background Field and Heisenberg-Euler Effective Action
• Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field