Newton–Leibniz integration for ket–bra operators (III)—Application in fermionic quantum statistics

The Newton–Leibniz integration over Dirac’s ket–bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480–494] is generalized to Newton–Leibniz–Berezin integration over fermionic ket–bra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac’s symbolic method for Fermi system can also be developed, which exhibits Bose-Fermi supersymmetry in this aspect.