We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...

Computers have emerged as essential tools in the modern scientific analysis and simulationbased design of complex physical systems. The deeply-seated abstraction of continuity immanent to many physical systems inherently clashes with a digital computer’s ability of storing and manipulating only finite sets of numbers. While there has been a number of computational techniques that proposed discr...

In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five dimensional U(1) gauge theory associated with StueckelbergSchrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five dimensional theory prevents a natural generalization of the Dirac monopole, since the theory is not symme...

In this paper we explore the idea of looking at the Dirac quantisation conditions as h̄-dependent constraints on the tangent bundle to phase-space. Starting from the path-integral version of classical mechanics and using the natural Poisson brackets structure present in the cotangent bundle to the tangent bundle of phasespace, we handle the above constraints using the standard theory of Dirac fo...

The effect of charge-carrier screening on the transport properties of a neutral graphene sheet is studied by directly probing its electronic structure. We find that the Fermi velocity, Dirac point velocity, and overall distortion of the Dirac cone are renormalized due to the screening of the electron-electron interaction in an unusual way. We also observe an increase of the electron mean free p...

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce , as in the symplectic analysis, a series of lagrange multiplie...

The Dirac quantization ‘procedure’ for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac s...

The band structure of strongly correlated two-dimensional (2D) semimetal systems is found to be significantly affected by the spin-orbit coupling (SOC), resulting in SOC-induced Fermi surfaces. Dirac, Weyl and Majorana representations are used for the description of different semimetals, though the band structures of all these systems are very similar. We develop a theoretical approach to the b...

We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as fourfold and sixfold rotational symm...

Dirac points with giant spin-orbit splitting in the electronic structure of two-dimensional transition-metal carbides, 2015, Physical Review B. Two-dimensional (2D) materials, especially their most prominent member, graphene, have greatly influenced many scientific areas. Moreover, they have become a base for investigating the relativistic properties of condensed matter within the emerging fiel...