Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras
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| Format: | Preprint |
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2018
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| _version_ | 1866911224610947072 |
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| author | Beygi, Alireza Klevansky, S. P. Bender, Carl M. |
| author_facet | Beygi, Alireza Klevansky, S. P. Bender, Carl M. |
| contents | 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 $η$, which are quadratically nilpotent ($η^2=0$), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: $ηη^{PT}+η^{PT}η=-1$, where $η^{PT}$ is the PT adjoint of $η$, and $ηη^{CPT}+η^{CPT}η=1$, where $η^{CPT}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1803_10034 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras Beygi, Alireza Klevansky, S. P. Bender, Carl M. Quantum Physics High Energy Physics - Theory Mathematical Physics 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 $η$, which are quadratically nilpotent ($η^2=0$), and algebras with PT and CPT adjoints can be constructed. These algebras obey different anticommutation relations: $ηη^{PT}+η^{PT}η=-1$, where $η^{PT}$ is the PT adjoint of $η$, and $ηη^{CPT}+η^{CPT}η=1$, where $η^{CPT}$ 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. |
| title | Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/1803.10034 |