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Three important properties of phonons may be deduced from this technique. First, phonons are bosons, since any number of identical excitations can be created by repeated application of the creation operator bk†. Second, each phonon is a "collective mode" caused by the motion of every atom in the lattice. This may be seen from the fact that the creation and annihilation operators, defined here in momentum space, contain sums over the position and momentum operators of every atom when written in position space. (See position and momentum space.)[2] Finally, using the position–position correlation function, it can be shown that phonons act as waves of lattice displacement.[citation needed]