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Conference Papers Year : 2008

Crypto-Hermiticity of nonanticommutative theories

A.V. Smilga
  • Function : Author
  • PersonId : 1076188
  • IdRef : 115657169


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.

Dates and versions

in2p3-00207914 , version 1 (18-01-2008)


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


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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