PT-symmetric representations of fermionic algebras
A recent paper by Jones-Smith and Mathur, Phys. Rev. A 82, 042101 (2010) extends PT-symmetric quantum mechanics from bosonic systems (systems for which T2=1) to fermionic systems (systems for which T2=−1). The current paper shows how the formalism developed by Jones-Smith and Mathur can be used to c...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
25 August 2011
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| In: |
Physical review. A, Atomic, molecular, and optical physics
Year: 2011, Volume: 84, Issue: 2, Pages: 1-5 |
| ISSN: | 1094-1622 |
| DOI: | 10.1103/PhysRevA.84.024102 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevA.84.024102 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevA.84.024102 
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| Author Notes: | Carl M. Bender and S.P. Klevansky |
| Summary: | A recent paper by Jones-Smith and Mathur, Phys. Rev. A 82, 042101 (2010) extends PT-symmetric quantum mechanics from bosonic systems (systems for which T2=1) to fermionic systems (systems for which T2=−1). The current paper shows how the formalism developed by Jones-Smith and Mathur can be used to construct PT-symmetric matrix representations for operator algebras of the form η2=0, ¯η2=0, η¯η+¯ηη=α1, where ¯η=ηPT=PTηT−1P−1. It is easy to construct matrix representations for the Grassmann algebra (α=0). However, one can only construct matrix representations for the fermionic operator algebra (α≠0) if α=−1; a matrix representation does not exist for the conventional value α=1. |
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| Item Description: | Gesehen am 16.03.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1094-1622 |
| DOI: | 10.1103/PhysRevA.84.024102 |