相关论文: SUSY transformations between digonalizable and non…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass…
We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants…
Brief review is given of my recent results on solvable models within the so called PT symmetric version of quantum mechanics.
In recent decades, an important shift has taken place with the growing role of non-Hermitian quantum mechanics. What makes this framework remarkable is that the eigenvalues of the Hamiltonians involved can still be real, just as in the…
The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock)…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
We recall the importance of recognizing the different mathematical nature of various concepts relating to PT-symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that…
The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C) or $A_1$. This leads to new types of both…
We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy…
In this work, we introduce a PT-symmetric infinite-dimensional representation of the Uz(sl(2,R)) Hopf algebra, and we analyse a multiparametric family of Hamiltonians constructed from such representation of the generators of this…
We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a…
The observation that PT-symmetric Hamiltonians can have real-valued energy levels even if they are non-Hermitian has triggered intense activities, with experiments, in particular, focusing on optical systems, where Hermiticity can be broken…
In this work we present symmetry transformations relating bosons to fermions which cannot be represented as a supersymmetric algebra. We present a symmetry transformation relating a complex scalar and a fermion in four dimensions and…
We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana…
We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the N = 2 SUSY quantum mechanical model of a one (0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY invariant…
We reelaborate on a general method for diagonalizing a wide class of nonlinear Hamiltonians describing different quantum optical models. This method makes use of a nonlinear deformation of the usual su(2) algebra and when some physical…
A conceptual bridge is provided between SUSY and the three-Hilbert-space upgrade of quantum theory a.k.a. ${\cal PT}-$symmetric or quasi-Hermitian. In particular, a natural theoretical link is found between SUSY and the presence of Kato's…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…