4.3. Fermionic creation and annihilation operators
In the previous section, we mentioned that the Fock space is a mathematical construction and does not represent a physical reality nor a chemical actuality. However, please keep in mind that in a molecule, each electron can occupy only one spin-orbit at a time and no two electrons can occupy the same spin-orbit.
Now we further consider a subspace of the Fock space, which is spanned by the occupation number of the spin-orbits, which is described by 
electronic basis states 
, where 
is the occupation number of orbital 
.
The spin-orbital state 
not occupied by an electron is represented by 
.
We define a set of fermionic annihilation operators 
and creation operators 
, which act on local electron modes, and which satisfy the following anti-commutation relations:
where 
is the Dirac delta function. The operators 
are called the occupation number operators and commute with one...