Cryptoreality of nonanticommutative Hamiltonians

University of Nantes, Naoned, Pays de la Loire, France
Journal of High Energy Physics (Impact Factor: 6.11). 03/2007; 2007(7). DOI: 10.1088/1126-6708/2007/07/036
Source: arXiv


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???eRHe?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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