相关论文: (1+1)-Dirac bound states in one-dimension; positio…
Bound states arising in Dirac fields are usually attributed to two kinds of features: domain walls where a real Dirac mass field changes sign, which host Jackiw-Rebbi states, and phase singularities in a complex Dirac mass field, which host…
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on…
Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory,…
Stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product at small values of gravitational…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…
The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The set of equations representing the Dirac equation in the Newman-Penrose formalism is decoupled into an axial and angular part. The axial equation, which is…
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space.…
We are dealing with boundary conditions for Dirac-type operators, i.e., first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators. We characterize (what we conjecture is)…
This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional p-adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
We consider a Dirac equation set on an extended spin space that contains fermion and boson solutions. At given dimension, it determines the scalar symmetries. The standard field equations can be equivalently written in terms of such degrees…
The classical and quantum dynamics of two particles constrained on $S^1$ is discussed via Dirac's approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also…
We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $ f(x,t) - i \mu \gamma^0 \Psi$, where both $f$ and $\Psi$ are…
We compare two different solutions of the Dirac equation in (1+1) dimensions. One solution is for a fermion in the presence of an electric potential and the other is for a fermion in the presence of a pseudoscalar potential. It is shown…