Moravcsik's theorem on complete sets of polarization observables reexamined

Minimal complete sets for two pseudoscalar meson photoproduction

“…However, these sets are slightly over complete since each observable depends on more than one bilinear product. According to the current knowledge [11,13] a truly minimal complete set consists of 2N observables. Thus the task remains to reduce the slightly over complete sets by eight observables while retaining the completeness.…”

“…In that way, one establishes a mathematical similarity with the shape-classes in single-meson photoproduction [8,13]. For shape-class II this would be:…”

“…The generalization to any odd number is the actual modification to Moravcsik's theorem. A proof of the original version of the theorem can be found in [12] and a quite detailed proof of the modified version of the theorem is given in reference [13].…”

“…The number of unique topologies is solely determined by the number of nodes (or edges), i.e. for N ≥ 3 it is N !/(2N ) [13].…”

“…This theorem allows for the extraction of complete sets of observables for an arbitrary number of amplitudes. Furthermore, due to its graph-theoretical foundation, the whole algorithm can be automated [13].…”