Abstract
A new generalized ModMax model of nonlinear electrodynamics with four parameters is proposed. The ModMax model and Born–Infeld-type electrodynamics are particular cases of the present model. It is shown that a singularity of the electric field at the center of point-like charged particles is absent. We found corrections to Coulomb's law at r→∞ and obtained the total electrostatic and magnetic energies of point-like charges. Free electric and magnetic charges and their densities are obtained.
Highlights
A new generalized ModMax model of nonlinear electrodynamics with four parameters is proposed
To smooth singularities we propose the generalized ModMax model with the Lagrangian density βλG2 2σ σ where L is given by Eq (1), β and λ have the dimensions of4 and σ is the dimensionless parameter
The Born–Infeld model is of interest because at the low energy D-brain dynamics is governed by Born–Infeld-type action [18], [19]
Summary
Are Lorentz invariants with B, E being the magnetic induction and electric fields correspondingly, Fμν = ∂μAν − ∂νAμ, Fμν = (1/2)ǫμναβFαβ is the dual electromagnetic field, and γ is the dimensionless parameter This model as well as Maxwell electrodynamics with the Lagrangian density LM = −F. where L is given by Eq (1), β and λ have the dimensions of (length) and σ is the dimensionless parameter. From Eq (9), for the source of the point-like charged particle with the electric charge q, in Gaussian units, we obtain the equation as follows It follows from Eq (16) that at u → 0, v(0) = 1 for σ < 1, or in terms of electric fields.
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