Euler-Heisenberg Lagrangian under an Axial Gauge Field

Patrick Copinger^1*, Koichi Hattori², Di-Lun Yang¹

¹Institute of Physics, Academia Sinica, Taipei, Taiwan
²Institute of Modern Physics, Zhejiang University, Zhejiang, China

* Presenter:Patrick Copinger, email:copinger0@gate.sinica.edu.tw

The Euler-Heisenberg Lagrangian supplemented with a constant axial gauge field in addition to the homogeneous electromagnetic field is discussed. I describe two exactly solvable setups by virtue of their eigenspectrum: one with a magnetic field and temporal axial gauge field (chiral chemical potential) and the other with an electric field and spatial axial gauge field. The spatial axial gauge field resembles a vorticity, thought important in heavy-ion collisions. I discuss in particular the latter case with electric field as the spatial axial gauge field is found to enhance the Schwinger effect, (or the spontaneous particle anti-particle production by a quantum field theoretic instability in a strong electric field). I furthermore discuss a derivation of the imaginary part of the Lagrangian stemming from the worldline formalism, in which I argue the enhancement occurs by a quadratic mass shift. Finally, I discuss the purely massless case, whose augmentation to the Lagrangian is a Chern-Simons term.
P.C., K. Hattori, and D.-L., Yang, [hep-th] 2208.12913 (2022).

Keywords: Schwinger Effect, Strong Field QED, Worldline Formalism, Finite Theta