  The electromagnetic current operator of a composite system must be a
relativistic vector operator satisfying current conservation, cluster
separability and the condition that interactions between the constituents do
not renormalize the total electric charge. Assuming that these interactions are
described in the framework of relativistic quantum mechanics of systems with a
fixed number of particles we explicitly construct the current operators
satisfying the above properties in cases of two and three particles and prove
that solutions exist for any number of particles. The consideration is
essentially based on the method of packing operators in the point form of
relativistic dynamics developed by Sokolov. Using the method developed by
Sokolov and Shatny we also construct the current operators in the instant and
front forms and prove that the corresponding results are physically equivalent.
The paper is self-contained what makes it possible for the reader to learn
both, relativistic quantum mechanics of systems with a fixed number of
particles and the problem of constructing the electromagnetic current operator
for such systems.
