Two- and four-dimensional representations of the PT- and CPT -symmetric fermionic algebras - Beygi, Alireza; Klevansky, Sandra Pamela; Bender, Carl M. (Physical review, 2018)
Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that T2=−1 for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators η, which are quadratically nilpotent (η2=0), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: ηηPT+ηPTη=−1, where ηPT is the PT adjoint of η, and ηηCPT+ηCPTη=1, where ηCPT is the CPT adjoint of η. This paper presents matrix representations for the operator η and its PT and CPT adjoints in two and four dimensions. A PT-symmetric second-quantized Hamiltonian modeled on quantum electrodynamics that describes a system of interacting fermions and bosons is constructed within this framework and is solved exactly.