Toroidal Multipole Moments in Classical Electrodynamics: An Analysis of their Emergence and Physical Significance
Stefan Nanz investigates the necessity for three multipole families in classical electrodynamics. He shows that by imposing symmetry and parity constraints, it is sufficient to deal with only two multipole families. This implies that the toroidal multipole moments do not represent an independent multipole family, and they only emerge in the long-wavelength limit.
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1 Introduction and Overview
2 Why another Multipole Family?
3 Basic Equations and Notations
4 Multipole Expansion of the Potentials
5 Direct Multipole Expansion of Electromagnetic Fields
6 Connection and Comparison of the Different Approaches
7 Summary and Outlook