The Logic of the Regular Charge-Monopole Theory

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The following points explain the logic used for the construction of the Regular Charge-Monopole Theory (RCMT).
  1. Historically, the theoretical structure of classical electrodynamics has been built on the basis of experimental data. Its main elements are Maxwell equations, the Lorentz law of force and the variational principle used for deriving these equations [1]. The system consists of electric charges and electromagnetic fields. It contains no monopole.

  2. A confirmation of the existence of magnetic monopoles has not been reported by experimenters. Therefore, a construction of a monopole theory must rely on theoretical arguments. The following mathematical transformations are used for this purpose:

    E → B,   B → −E,   e → g,   g → − e,

    where g denotes the monopole strength. These relations are called duality transformations.

  3. An application of these transformations to Maxwellian electrodynamics of electric charges and electromagnetic fields yields a theory of monopoles and electromagnetic fields. This theory holds for systems that contain no electric charge. Hence, the next problem is to construct a unified charge-monopole theory that is consistent with two sub-theories: for systems of charges without monopole, it must agree with the ordinary Maxwellian electrodynamics; for systems of monopoles without charges it must agree with the dual theory described above.

  4. The RCMT theory is derived in [2] and, alternatively, in [3]. If you are familiar with the first 100 pages of [1] then you can read these articles quite easily. You can find there a regular Lagrangian for the particles, a regular Lagrangian density for the fields, the corresponding equations of motion and the fields' energy-momentum tensor.

  5. An application of the RCMT to the physical world is described in [4,5].
References:

[1] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Elsevier, Amsterdam, 2005).

[2] E. Comay, Nuovo Cimento 80B, 159 (1984).

[3] E. Comay, Nuovo Cimento 110B, 1347 (1995).

[4] E. Comay, Elect. J. Theor. Phys., 9, 93 (2012).

[5] E. Comay, in Has the Last Word been Said on Classical Electrodynamics?, (Rinton Press, NJ, 2004)..