Born-Infeld Electrodynamics and Euler-Heisenberg-like Model: outstanding examples of the lack of commutativity among quantized truncated actions and truncated quantized actions
arXiv:0912.2321 · doi:10.1142/S0217751X10051219
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 ($ {\raise0.7ex\hbox{$1$} \mathord{\left/ {\vphantom {1 {r^5}}}\right.\kern-\nulldelimiterspace} \lower0.7ex\hbox{${r^5}$}}$-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.
7 pages. Title changed, revised version. To appear in Int. J. Mod. Phys. A
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