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Crypto-Hermiticity of nonanticommutative theories

Abstract : We note that, though nonanticommutative 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 crypto-Hermitian (or quasi-Hermitian) Hamiltonians having attracted recently a considerable attention. They can be made manifestly Hermitian via the similarity transformation H -> e^R H e^{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one though it is difficult in some cases to write explicit expressions for a half of supercharges. The deformed SQM models make perfect sense. It is not clear whether it is also the case for NAC Minkowski field theories -- the conventionally defined S--matrix is not unitary there.
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http://hal.in2p3.fr/in2p3-00207914
Contributor : Dominique Girod <>
Submitted on : Friday, January 18, 2008 - 3:11:54 PM
Last modification on : Friday, January 11, 2019 - 10:31:27 AM

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  • HAL Id : in2p3-00207914, version 1
  • ARXIV : 0801.2686

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A.V. Smilga. Crypto-Hermiticity of nonanticommutative theories. International Workshop on Supersymmetry and Quantum Symmetries, SQS'07, Jul 2007, Dubna, Russia. ⟨in2p3-00207914⟩

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