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arXiv · hep-th/0703038

Cryptoreality of nonanticommutative Hamiltonians

E. A. Ivanov·A. V. Smilga
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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.

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E. A. Ivanov, A. V. Smilga. 2007-03-05. Cryptoreality of nonanticommutative Hamiltonians. https://doi.org/10.1088/1126-6708%2F2007%2F07%2F036

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