We shall look in detail at four special cases where A ^ ^ and B ^ ^ are equal to creation and annihilation operators. For N particles we'll denote the creation operators by a ^ ^ i † † and the annihilation operators by a ^ ^ i ( i = 1 , 2 , 3 , … … , N ) . They satisfy the commutation relations for bosonic operators [ a ^ ^ i , a ^ ^ j † † ] = δ δ i j 1 ^ ^ , or the anti-commutation relations for fermionic operators { a ^ ^ i , a ^ ^ j † † } = δ δ i j 1 ^ ^ where δ δ i j denotes the Kronecker delta and 1 ^ ^ denotes the identity operator.