San José State University 

appletmagic.com Thayer Watkins Silicon Valley & Tornado Alley USA 



For the case of fermions it is the anticommutator of two operations that must be considered. The anticommutator of two operations, P and Q, is defined as
Let F be an operator and F* be its adjoint. The canonical quantification conditions to be satisfied by F and F* are
where 0^ is the zero operator, the operator that maps any function to the zero function.
Note that {F, F*}=I implies that
The condition that {F, F}=0^ and hence {F*, F*}=0^ is new for the case of the anticommutator, but [P, P]=0^ is automatically satisfied any operator P for the commutator. The conditions that {F, F}=0^ and {F*, F*}=0^ imply that FF=0^ and F*F*=0^.
Consider now
Let Φ be an eigenfunction of F*F.
This means that
Thus a fermion state can have at most one particle. This is the Pauli Exclusion Principle.
HOME PAGE OF Thayer Watkins 