2.3: System of identical fermions and bosons

The Hilbert space ¡bxif,,' (3.33) for a system of r¿ identical fermions each with spin s and nr identica.l bosons e¿rch with spin .s' is the direct product of the n-ferrnion and zt-boson Hilbert 28 spaces. Thar is, ¡å*i.i,,=t*;ø¿*;i (3.34) /'*;,,';,, ¡ spanned by vecrors of the form (3.35) where I rr{rr¡rr2 ..} > ir the Slate¡ dererminant (3.7) and I ntþl.,ntr...l > is the symmetric determinant (3.23).