A complete multipole expansion for a test particle in geometric fields

We study the motion of a test particle interacting with a class of external fields including torsion, curvature, electromagnetic and Yang–Mills fields, using the definition of total energy momentum, angular momentum, charge and isotopic spin introduced in a preceding paper. We define a set of reduced multipole moments and we show that they give a complete description of the density and the flow of the quantities mentioned above. We write explicitly the exact evolution equations in terms of the reduced multipole moments and we show that they are the only consequences of the balance equations.