# Cryptoreality of nonanticommutative Hamiltonians

@article{Ivanov2007CryptorealityON,
title={Cryptoreality of nonanticommutative Hamiltonians},
author={Evgeny Ivanov and Andrei V. Smilga},
journal={Journal of High Energy Physics},
year={2007},
volume={2007},
pages={036-036}
}
• Published 5 March 2007
• Physics
• Journal of High Energy Physics
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…
16 Citations

## Figures from this paper

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by
• Physics, Mathematics
• 2006
We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a
We discuss the Hamiltonian H = p2/2 − (ix)2n+1 and the mixed Hamiltonian Hmixed = (p2 + x2)/2 − g(ix)2n+1. The Hamiltonians H and in some cases also Hmixed are crypto-Hermitian in a sense that, in
We note that when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the
• Mathematics
• 2008
We construct type IIB supergravity duals of non-anticommutative deformed = 4 SU(N) gauge theories. We consider in particular deformations preserving = (1, 0) and = (1/2, 0) supersymmetry. Such
We consider the Dirac operator on a 2-sphere without one point in the case of non-integer magnetic flux. We show that the spectral problem for the Hamiltonian (the square of Dirac operator) can
• Physics, Mathematics
• 2009
AbstractThe $$\mathcal{N}$$-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to
• Physics
• 2008
We review the non-anticommutative Q-deformations of N=(1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann
• Physics
• 2012
The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the

## References

SHOWING 1-10 OF 50 REFERENCES

• Mathematics
• 2005
We study nonanticommutative deformations of N = 2 two-dimensional eu- clidean sigma models. We flnd that these theories are described by simple deformations of Zumino's lagrangian and the holomorphic
• Physics
• 2006
We consider non(anti)commutative (NAC) deformations of d = 1 = 2 superspace. We find that, in the chiral base, the deformation preserves only a half of the original (linearly realized) supercharge
• Mathematics
• 2003
Non commutative superspaces can be introduced as the Moyal-Weyl quan- tization of a Poisson bracket for classical superflelds. Difierent deformations are studied corresponding to constant background
We develop a gauged Wess–Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended N=1∕2 supersymmetry written over
• Mathematics
• 2003
We investigate the most general non(anti)commutative geometry in N = 1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial
We deform the standard four dimensional = 1 superspace by making the odd coordinates θ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of
• Mathematics
• 2000
We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a
• Mathematics
• 1998
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new
• Physics
• 2003
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space–time reflection symmetry (PT