Related papers: Higher Derivative Fermionic Field Equation in the …
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
For one dimensional motions, we derive from the Dirac Spinors Equation (DSE) the Quantum Stationary Hamilton-Jacobi Equation for particles with spin 1/2. Then, We give its solution. We demonstrate that the $QSHJES_{1\over2}$ have two…
Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two…
We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
In this paper, we show that a system of localized particles, satisfying the Fermi statistics and subject to finite-range interactions, can be exactly solved in any dimension. In fact, in this case it is always possible to find a finite…
We consider a lattice model of itinerant electrons coupled to an array of localized classical Heisenberg spins. The nature of the ground state ordered magnetic phases that result from the indirect spin-spin coupling mediated by the…
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 analyse the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP) equation. Since the KDP--equation which describes spin-0 and spin-1 bosons is of Dirac-type, we examine some analogies and differences from the Dirac equation. The…
The Dirac equation for charged and neutral fermions with anomalous magnetic moments is solved in a uniform magnetic field. We find the relativistic wave functions and energy spectra. In the non-relativistic limit the wave functions and…
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic…
We derive an equivalent traveling wave form description for Dirac field. In the non-relativistic limit, such form can reduce to inverse-Galilean transformed Schrodinger-type equation. We find that, the resulting two-component…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all…
The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…
The virial and the Hellmann--Feynman theorems for massless Dirac electrons in a solid are derived and analyzed using generalized continuity equations and scaling transformations. Boundary conditions imposed on the wave function in a finite…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies…
Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer Duffin equations for particles of…