Cryptoreality of nonanticommutative Hamiltonians

TL;DR

This paper shows that nonanticommutative deformations of supersymmetric theories, which appear non-Hermitian, are actually cryptoreal and can be transformed into Hermitian form, preserving supersymmetry algebra.

Contribution

It demonstrates that NAC deformed Hamiltonians are cryptoreal and can be made Hermitian, extending the concept to quantum mechanics and 4D field models.

Findings

NAC deformations lead to non-Hermitian Hamiltonians that are cryptoreal.

Such Hamiltonians can be transformed into Hermitian form via similarity transformations.

Supersymmetry algebra remains intact under NAC deformations.

Abstract

We note that, though nonanticommutative (NAC) deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of ``cryptoreal'' Hamiltonians considered recently by Bender and collaborators. They can be made manifestly Hermitian via the similarity transformation H -> exp{R} H exp{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one, though being realized differently on the involved canonical variables. Besides quantum-mechanical models, we treat, along similar lines, some NAC deformed field models in 4D Minkowski space.