Here S ν ν is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic ( ν ν = + ) or fermionic ( ν ν = − − ) statistics, and the overline represents the completion of the space. The bosonic (resp. fermionic) Fock space can alternatively be constructed as (the Hilbert space completion of) the symmetric tensors F + ( H ) = S ∗ ∗ H ¯ ¯ (resp. alternating tensors F − − ( H ) = ⋀ ⋀ ∗ ∗ H ¯ ¯ ). For every basis for H there is a natural basis of the Fock space, the Fock states.