PT-symmetric representations of fermionic algebras

Carl M. Bender and S. P. Klevansky
Phys. Rev. A 84, 024102 – Published 25 August 2011

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 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, η¯2=0, ηη¯+η¯η=α1, where η¯=ηPT=PTηT1P1. 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 (α0) if α=1; a matrix representation does not exist for the conventional value α=1.

  • Figure
  • Figure
  • Received 27 April 2011

DOI:https://doi.org/10.1103/PhysRevA.84.024102

©2011 American Physical Society

Authors & Affiliations

Carl M. Bender1,* and S. P. Klevansky2,†

  • 1Physics Department, Washington University, St. Louis, Missouri 63130, USA
  • 2Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany

  • *cmb@wustl.edu
  • spk@physik.uni-heidelberg.de

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Vol. 84, Iss. 2 — August 2011

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