Related papers: Applications of the nilpotent Dirac state vector
Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schroedinger's postulated wave-function rule for the operator quantization of the particle's canonical three-momentum, taken together with…
Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…
In this paper, we consider the Dirac-Coulomb equation for many-particles, to describe the interaction between electrons in the system having many electrons. The four-component wave function will expanding into a finite basis-set, using…
We briefly describe our relativistic quark-diquark model, developed within the framework of point form dynamics, which is the relativistic extension of the interacting quark-diquark model. In order to do that we have to show the main…
The influence of $\Delta$ isobar components on the ground state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations, and binding energies are…
We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and…
We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions to those of a cubic non-linear Dirac equation, given that the…
The generalized Dirac equation of the second order, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections are obtained. The first order…
Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…
The structure of the 1/Nc expansion for the baryon distribution amplitude in QCD is tested using quark models. Earlier conjectures about this structure based on the evolution equation and on the soft-pion theorem are confirmed by the model…
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
The virial theorem is applied to graphene and other Dirac Materials for systems close to the Dirac points where the dispersion relation is linear. From this, we find the exact form for the total energy given by $E = \mathcal{B}/r_s$ where…
We study the electroweak properties of ground state octet baryons in a relativistic quark-spectator-diquark model, with light-front formalism applied to take relativistic effects into account. Our model provides a consistent picture of the…
Poincare covariant quark models of the the nucleon, the $\Delta$ resonance and their excitations are explored. The baryon states are represented by eigenfunctions of the four-velocity and a confining mass operator, which reproduces the…
We study the baryonic fluctuations of electric charge, baryon number and strangeness, by considering a realization of the Hadron Resonance Gas model in the light flavor sector of QCD. We elaborate on the idea that the susceptibilities can…
Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the…
Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be…
In this thesis a model framework for describing baryons as diquark-quark bound states is presented which is formulated in an explicitly covariant manner. The relativistic bound state problem for three quarks is considered. Diquarks are…
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
Reformulation of Dirac equation in terms of real quadratic division algebra of quaternions is given. Similar equations with different mass term are identified as suitable for description of free propagating quark motion. The complete…