Two- and four-dimensional representations of the PT- and CPT-symmetric fermionic algebras

2018/03/27 by Beygi, Alireza, Klevansky, S. P., Bender, Carl M.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1803.10034

Abstract

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: ηη^PT+η^PTη=-1, where η^PT is the PT adjoint of η, and ηη^CPT+η^CPTη=1, where η^CPT 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.

Related

• PT symmetric fermionic particle oscillations in even dimensional representations
• Non-standard quantum algebras and finite dimensional PT-symmetric systems
• On the real matrix representation of PT-symmetric operators
• Geometry of PT-symmetric quantum mechanics
• The interplay of supersymmetry and PT symmetry in quantum mechanics: a case study for the Scarf II potential