Abstract
A theory of electromagnetism with higher order derivatives, which attained by generalizing the laws of electrostatics, laws that follow from the generalized Coulomb's law and the superposition principle, so that they are consistent with special relativity.
Highlights
The interest in theories with higher order derivatives has occupied the attention of physicists since the adoption of differential equations as a mechanism for describing physical systems (SALES; GIROTTO, 2021)
Despite the interest in using these theories and it never been forgotten over time, it was considered purely academic (SALES,1995)
With the advent of supersymmetry and string theory, the higher order theories have lost their academic stamp and the interest in them has increased. This is easy to understand, since both in supersymmetry, in its formulation in terms of super fields (BARCELOS, 1989, 1991a, 1991b), and in important examples in string theory (POLYAKOV, 1986), higher order derivatives occurred in abundance
Summary
The interest in theories with higher order derivatives has occupied the attention of physicists since the adoption of differential equations as a mechanism for describing physical systems (SALES; GIROTTO, 2021). Where Fμv = ∂vAμ − ∂μAv and a is a constant with length dimension This Lagrangian generates a linear field theory, with gauge symmetry of the type U(1), which reduces to Maxwell's theory when a = 0. This is a higher-order theory since the equations of motion derived from (1) contain quartic derivatives of the vector potential. Like Maxwell's theory, Podolsky's theory has definite positive energy in the electrostatic case, which, is finite for a point charge. This last result clearly shows that the force between two-point charges is no longer Coulombian, a point that deserves to be analysed more closely. Equations (19) and (20) are the fundamental laws of Podolsky's electrostatics and will be generalized later using special relativity
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