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 ($...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
27 Mar 2018
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| In: |
Arxiv
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| Online-Zugang: | Verlag, Volltext: http://arxiv.org/abs/1803.10034
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| Verfasserangaben: | Alireza Beygi, S.P. Klevansky, and Carl M. Bender |
MARC
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| 245 | 1 | 0 | |a Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras |c Alireza Beygi, S.P. Klevansky, and Carl M. Bender |
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| 520 | |a 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. | ||
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