Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 14

We denote N the state space of a system of N distinguishable particles, which is the tensor product of N individual state spaces ₁:

(A-1)

Two sub-spaces of N are particularly important for identical particles, as they contain all their accessible physical states: the space S(N) of the completely symmetric states for bosons, and the space A(N) of the completely antisymmetric states for fermions. The projectors onto these two sub-spaces are given by relations (B-49) and (B-50) of Chapter XIV:

(A-2)

and:

(A-3)

where the Pα are the N! permutation operators for the N particles, and εα the parity of Pα (in this chapter we have added for clarity the index N to the projectors S and A defined in Chapter XIV).