Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras
Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that $T^2=-1$ for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators $\eta$, which are quadratically nilpotent ($...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
27 Mar 2018
|
| In: |
Arxiv
|
| Online Access: | Verlag, Volltext: http://arxiv.org/abs/1803.10034
|
| Author Notes: | Alireza Beygi, S.P. Klevansky, and Carl M. Bender |
| Summary: | Fermionic systems differ from their bosonic counterparts, the main difference with regard to symmetry considerations being that $T^2=-1$ for fermionic systems. In PT-symmetric quantum mechanics an operator has both PT and CPT adjoints. Fermionic operators $\eta$, which are quadratically nilpotent ($\eta^2=0$), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: $\eta\eta^{PT}+\eta^{PT}\eta=-1$, where $\eta^{PT}$ is the PT adjoint of $\eta$, and $\eta\eta^{CPT}+\eta^{CPT}\eta=1$, where $\eta^{CPT}$ is the CPT adjoint of $\eta$. This paper presents matrix representations for the operator $\eta$ 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. |
|---|---|
| Item Description: | Gesehen am 05.11.2020 |
| Physical Description: | Online Resource |