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 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), an...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
28 March 2018
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| In: |
Physical review
Year: 2018, Volume: 97, Issue: 3 |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/PhysRevA.97.032128 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevA.97.032128 Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevA.97.032128 
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| 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 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. |
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| Item Description: | Gesehen am 05.11.2020 |
| Physical Description: | Online Resource |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/PhysRevA.97.032128 |