Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones

Abstract

Using a method based on the generating functional plus a kind of "correspondence principle" --- which acts as a bridge between the electromagnetic and scalar fields --- it is shown that the interparticle potential energy concerning a given $D$-dimensional electromagnetic model can be obtained in a simple way from that related to the corresponding scalar system. The $D$-dimensional electromagnetic potential for a general model containing higher derivatives is then found from the corresponding scalar one and the behavior of the former is analyzed at large as well as small distances. In addition, we investigate the presence of ghosts in the four-dimensional version of the potential associated with the model above and analyze the reason why the Coulomb singularity is absent from this system. The no-go theorem by Ostrogradski is demystified as well.

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• Spin- and velocity-dependent non-relativistic potentials in modified electrodynamics
• Renormalizability in $D$-dimensional higher-order gravity
• Fermion inter-particle potentials in 5D and a dimensional restriction prescription to 4D
• Quantum corrected gravitational potential beyond monopole-monopole interactions
• The Ultraviolet and Infrared Behavior of an Abelian Proca Model From the Viewpoint of a One-Parameter Extension of the Covariant Heisenberg Algebra