The commutation relations are simply carried over to infinite dimensions [ S i , S j ] = i ℏ ℏ S k ε ε i j k . S 2 is now equal to S 2 = ∑ ∑ m = 1 n S m 2 where n=∞. Its eigenvalue is S 2 | s , m >= s ( s + 1 ) ℏ ℏ 2 | s , m > . Defining the magnetic quantum number, angular momentum projected in the z direction, is more challenging than the simple state of spin. The problem becomes analogous to moment of inertia in classical mechanics and is generalizable to n dimensions. It is this property that allows for the creation and annihilation of bosons.