The Heisenberg-Euler Effective Action: 75 years on

Reissner-Nordström black holes in the inverse electrodynamics model

“…Furthermore, by replacing the Lagrangian density (3), and the metric and electromagnetic tensors (7) and ( 8) in the energy-momentum tensor definition (6), the non zero components of the latter tensor can be found. Together with the metric tensor above (7), these components enable the resolution of the field equations (10) yielding…”

“…With this expression, the gauge invariants ( 9) can be simplified reading X = E(r) 2 − B(r) 2 and Y = 2E(r) • B(r), i.e., the usual gauge invariants in standard Electrodynamics are recovered. Moreover, we can replace (11) in the field equations (10), achieving the expressions…”

“…Nonlinear models have also been studied from the point of view of effective Lagrangians which attempt to describe Quantum Electrodynamics [6]. Some important examples of these kinds of theories are the Born-Infeld [7,8] and the Euler-Heisenberg models [9][10][11][12][13][14]. Following this line of reasoning, in the last years, different works have studied modified Electrodynamics models coupled with gravity [15].…”

One-loop calculations in Lorentz-breaking theories and proper-time method

“…[3]). One of the most convenient versions of the proper-time method is the one based on the use of the zetafunction regularization and Gaussian-like integrals [4] which was shown to be efficient for obtaining the Heisenberg-Euler (HE) action for a scalar QED in a Lorentz-invariant case and its supersymmetric extension (a general review on the HE effective action can be found in [5]).…”

Photon merging and splitting in electromagnetic field inhomogeneities

“…The vacuum of quantum electrodynamics (QED) acquires properties akin to those of ordinary polarizable matter when subjected to strong electromagnetic fields [1][2][3]. These fields can couple to electron-positron fluctuations inducing nonlinear interactions (for reviews, see [4][5][6][7][8][9][10][11][12]). The spatial and temporal scale associated to these electron-positron fluctuations is set by the Compton wavelength λ C = 1/m ≈ 3.86 × 10 −13 m and the Compton time τ C = 1/m ≈ 1.29 × 10 −21 s of the electron respectively, where m ≈ 511keV denotes the electron mass.…”