We calculate the lowest-order corrections to the static potential for both the generalized BornInfeld electrodynamics and an EulerHeisenberg-like model, in the presence of a constant external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a long-range correction (1/r5-type) to the Coulomb potential for the generalized BornInfeld electrodynamics. Interestingly enough, in the EulerHeisenberg-like model, the static potential remains Coulombian. Therefore, contrary to popular belief, the quantized truncated action and the truncated quantized action do not commute at all. © 2010 World Scientific Publishing Company.
Accioly, A., Gaete, P., & HelaŸel-Neto, J. A. (2010). Born-infeld electrodynamics and eulerheisenberg-like model: Outstanding examples of the lack of commutativity among quantized truncated actions and truncated quantized actions. International Journal of Modern Physics A, 5951-5961. https://doi.org/10.1142/S0217751X10051219