We consider both generalized Born-Infeld and exponential electrodynamics. The field energy of a pointlike charge is finite only for Born-Infeld-like electrodynamics. However, both Born-Infeld-type and exponential electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in longrange (1/r 5 -type) corrections to the Coulomb potential. Once again, for their noncommutative versions, the interaction energy is ultraviolet finite.
We show that one can obtain naturally the confinement of static charges from
the spontaneous symmetry breaking of scale invariance in a gauge theory. At the
classical level a confining force is obtained and at the quantum level, using a
gauge invariant but path-dependent variables formalism, the Cornell confining
potential is explicitly obtained. Our procedure answers completely to the
requirements by 't Hooft for ''perturbative confinement''.Comment: 6 page
For a theory with a pseudo scalar coupling φFF and in the case that there is a constant electric or magnetic strength expectation value, we compute the interaction potential within the structure of the gauge-invariant but pathdependent variables formalism. While in the case of a constant electric field strength expectation value the static potential remains Coulombic, in the case of a constant magnetic field strength the potential energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static charges.
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