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Title: PT-symmetric representations of fermionic algebras

Abstract

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 T{sup 2}=1) to fermionic systems (systems for which T{sup 2}=-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 {eta}{sup 2}=0, {eta}{sup 2}=0, {eta}{eta}+{eta}{eta}={alpha}1, where {eta}={eta}{sup PT}=PT{eta}T{sup -1}P{sup -1}. It is easy to construct matrix representations for the Grassmann algebra ({alpha}=0). However, one can only construct matrix representations for the fermionic operator algebra ({alpha}{ne}0) if {alpha}=-1; a matrix representation does not exist for the conventional value {alpha}=1.

Authors:
 [1];  [2]
  1. Physics Department, Washington University, St. Louis, Missouri 63130 (United States)
  2. Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
22068590
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 2; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; BOSON-FERMION SYMMETRY; FERMIONS; MATRICES; QUANTUM MECHANICS

Citation Formats

Bender, Carl M, and Klevansky, S P. PT-symmetric representations of fermionic algebras. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.024102.
Bender, Carl M, & Klevansky, S P. PT-symmetric representations of fermionic algebras. United States. https://doi.org/10.1103/PHYSREVA.84.024102
Bender, Carl M, and Klevansky, S P. 2011. "PT-symmetric representations of fermionic algebras". United States. https://doi.org/10.1103/PHYSREVA.84.024102.
@article{osti_22068590,
title = {PT-symmetric representations of fermionic algebras},
author = {Bender, Carl M and Klevansky, S P},
abstractNote = {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 T{sup 2}=1) to fermionic systems (systems for which T{sup 2}=-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 {eta}{sup 2}=0, {eta}{sup 2}=0, {eta}{eta}+{eta}{eta}={alpha}1, where {eta}={eta}{sup PT}=PT{eta}T{sup -1}P{sup -1}. It is easy to construct matrix representations for the Grassmann algebra ({alpha}=0). However, one can only construct matrix representations for the fermionic operator algebra ({alpha}{ne}0) if {alpha}=-1; a matrix representation does not exist for the conventional value {alpha}=1.},
doi = {10.1103/PHYSREVA.84.024102},
url = {https://www.osti.gov/biblio/22068590}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 84,
place = {United States},
year = {Mon Aug 15 00:00:00 EDT 2011},
month = {Mon Aug 15 00:00:00 EDT 2011}
}