PT-symmetric representations of fermionic algebras - Bender, Carl M.; Klevansky, Sandra Pamela (Physical review. A, Atomic, molecular, and optical physics, 2011)
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.
Gesehen am 16.03.2022