Degrees of Freedom in a Multipole Expansion of an Electromagnetic Current Over a Worldline

Spasova, Vanya and Gratus, Jonathan (2022) Degrees of Freedom in a Multipole Expansion of an Electromagnetic Current Over a Worldline. Masters thesis, Lancaster University.

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Abstract

We are investigating the free components of an electromagnetic current, which we describe as a De Rham current over an arbitrary worldline on an arbitrary spacetime MST . These calculations are an extension of a previous research done on dipoles and quadrupoles, in which they are described in a metric-free manner. In this thesis, we consider an adapted coordinate system to define the free components of an electromagnetic distribution over an arbitrary worldline and extend the previous work done by going up to the octupole order of the electromagnetic current expansion. Using the symmetries of the components found in the calculations, we derive a generalized expression for the number of free components of any 2^k-tupole current, which satisfies the equation which leads to conservation of charge, dJ = 0.