Related papers: Pseudo Hermitian interactions in the Dirac Equatio…
We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show…
In paper within the model with a maximal mass M and with use of anti de Sitter space is considered the Dirac equation properties for a fermion of mass m on the mass surface. The paper shows that free Hamiltonian and Hamiltonian with…
We study generalized Dirac oscillators with complex interactions in $(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $\eta$ pseudo Hermitian with respect to certain metric…
We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac…
The Dirac equation in $(2+1)$ dimensions on the toroidal surface is studied for a massless fermion particle under the action of external fields. Using the covariant approach based on general relativity, the Dirac operator stemming from a…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. The spectrum and the exact solutions of the time dependent non-Hermitian and angle…
It is of general theoretical interest to investigate the properties of superluminal matter wave equations for spin one-half particles. One can either enforce superluminal propagation by an explicit substitution of the real mass term for an…
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…
By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac…
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This…
We extend the definition of eta-weak-pseudo-Hermiticity to the class of potentials endowed with position-dependent mass. The construction of non-Hermitian Hamiltonians through some generating function are obtained. Special cases of…
Solutions to the Dirac equation are constructed for a massless charged fermion in Coulomb and Aharonov--Bohm potentials in 2+1 dimensions. The Dirac Hamiltonian on this background is singular and needs a one-parameter self-adjoint…
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…
The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the…
The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three…
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it…
We consider several classes of symmetries of the Dirac Hamiltonian in 3+1 dimensions, with axially-deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when…
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…
A class of non-Hermitian d-dimensional Hamiltonias with position dependent mass and their $\eta$-pseudo-Hermiticity generators is presented. Illustrative examples are given in 1D, 2D, and 3D for different position dependent mass settings.