Born-Infeld Electrodynamics and Euler-Heisenberg-like Model: outstanding examples of the lack of commutativity among quantized truncated actions and truncated quantized actions

الأصل · EN

We calculate the lowest-order corrections to the static potential for both the generalized Born-Infeld Electrodynamics and an Euler-Heisenberg-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 (0.7ex1 / 1 r⁵.- 0.7exr⁵-type) to the Coulomb potential for the generalized Born-Infeld Electrodynamics. Interestingly enough, in the Euler-Heisenberg-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.