Two operators of great importance are the creation and annihilation operators, which upon acting on a Fock state add or respectively remove a particle in the ascribed quantum state. They are denoted a † † ( ϕ ϕ ) for creation and a ( ϕ ϕ ) for annihilation respectively. To create ("add") a particle, the quantum state | ϕ ϕ ⟩ ⟩ is symmetric or exterior- multiplied with | ϕ ϕ ⟩ ⟩ ; and respectively to annihilate ("remove") a particle, an (even or odd) interior product is taken with ⟨ ⟨ ϕ ϕ | , which is the adjoint of a † † ( ϕ ϕ ) . It is often convenient to work with states of the basis of H so that these operators remove and add exactly one particle in the given basis state. These operators also serve as generators for more general operators acting on the Fock space, for instance the number operator giving the number of particles in a specific state | ϕ ϕ i ⟩ ⟩ is a † † ( ϕ ϕ i ) a ( ϕ ϕ i ) .