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Cryptoreality of nonanticommutative Hamiltonians

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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http://hal.in2p3.fr/in2p3-00149615
Contributor : Dominique Girod <>
Submitted on : Monday, May 28, 2007 - 9:31:05 AM
Last modification on : Thursday, February 7, 2019 - 3:47:01 PM

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E.A. Ivanov, A.V. Smilga. Cryptoreality of nonanticommutative Hamiltonians. Journal of High Energy Physics, Springer, 2007, 07, pp.036. ⟨10.1088/1126-6708/2007/07/036⟩. ⟨in2p3-00149615⟩

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