On Invariants of the Rotation Group

Any quantity transforming according to an irreducible representation of the space rotation group may be realized in three forms: i) as a multispinor χ   α   1… α 2l ; ii) as a 3‐tensor t   i   1… i l (for 2l even) or, tensor‐spinor t   αi   1… i l −1/2 (for 2l odd); iii) as an l ‐spinor Ψλ (l) (λ = − l ,…, l ). Only one invariant may be constructed of three quantitites of a given kind; so the three invariants are equal up to a numerical factor that is found in the work. A number of invariants may be constructed of four quantities, not all of them independent. For applications it is of importance to be able to construct an independent set of invariants of every kind, as well as to relate the invariants of different kinds. This problem is solved in the present work for arbitrary angular momenta l 1 , l 2 , l 3 , l 4 .