Cryptoreality of nonanticommutative Hamiltonians

Journal of High Energy Physics (Impact Factor: 6.22). 03/2007; DOI: 10.1088/1126-6708/2007/07/036
Source: arXiv

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. Comment: 15 pages, 2 figures

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