The map a : f → → a ( f ) from H to the bosonic CCR algebra is required to be complex antilinear (this adds more relations). Its adjoint is a † † ( f ) , and the map f → → a † † ( f ) is complex linear in H. Thus H embeds as a complex vector subspace of its own CCR algebra. In a representation of this algebra, the element a ( f ) will be realized as an annihilation operator, and a † † ( f ) as a creation operator.