Article
Cryptoreality of nonanticommutative Hamiltonians
Journal of High Energy Physics (Impact Factor: 6.22). 03/2007; DOI: 10.1088/11266708/2007/07/036
Source: arXiv

Article: Supersymmetry versus ghosts
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ABSTRACT: 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 nontrivial algebra. This allows one to obtain the exact solution both in the classical and quantum cases. The supercharges Q and are not Hermitially conjugate to each other anymore, which allows for the presence of negative energies in the spectrum. We show that the spectrum of the Hamiltonian is unbounded from below. It is discrete and infinitely degenerate in the free oscillatorlike case and becomes continuous running from −∞ to ∞ when interactions are added. Notwithstanding the absence of the ground state, there is no collapse, which suggests that a unitary evolution operator may be defined.Journal of Mathematical Physics 04/2008; 49(4). · 1.18 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the Dirac operator on S2 without one point in the case of noninteger magnetic flux. We show that the spectral problem for H = 2 can be well defined, if including in the Hilbert space H only nonsingular on S2 wave functions. However, this Hilbert space is not invariant under the action of — for certain ψ∈H, ψ does not belong to H anymore. This breaks explicitly the supersymmetry of the spectrum. In the integer flux case, supersymmetry can be restored if extending the Hilbert space to include locally regular sections of the corresponding fiber bundle. For noninteger fluxes, such an extension is not possible.Journal of Mathematical Physics 04/2012; 53(4). · 1.18 Impact Factor 
Article: Supersymmetry vs ghosts
11/2006;
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