BORN–INFELD ELECTRODYNAMICS AND EULER–HEISENBERG-LIKE MODEL: OUTSTANDING EXAMPLES OF THE LACK OF COMMUTATIVITY AMONG QUANTIZED TRUNCATED ACTIONS AND TRUNCATED QUANTIZED ACTIONS

Abstract

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 ([Formula: see text]-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.