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Part-I Dima (Int. J. Theor. Phys. 55, 949, 2016) of this paper showed in a representation independent way that gamma(0) is the Bergmann-Pauli adjunctator of the Dirac {gamma(mu)} set. The distiction was made between similarity (MA...
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Part-I Dima (Int. J. Theor. Phys. 55, 949, 2016) of this paper showed in a representation independent way that gamma(0) is the Bergmann-Pauli adjunctator of the Dirac {gamma(mu)} set. The distiction was made between similarity (MATH) transformations and PHYS transformations-related to the (covariant) transformations of physical quantities. Covariance is due solely to the gauging of scalar products between systems of reference and not to the particular action of gamma(0) on Lorentz boosts - a matter that in the past led inadvertently to the definition of a second scalar product (the Dirac-bar product). Part-II shows how two scalar products lead to contradictions and eliminates this un-natural duality in favour of the canonical scalar product and its gauge between systems of reference. What constitutes a proper observable is analysed and for instance spin is revealed not to embody one (except as projection on the boost direction - helicity). A thorough investigation into finding a proper-observable current for the theory shows that the Dirac equation does not possess one in operator form. A number of problems with the Dirac current operator are revealed - its Klein-Gordon counterpart being significantly more physical. The alternative suggested is finding a current for the Dirac theory in scalar form j(mu) = (psi) nu(mu)(psi).
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In the present paper, we solve the one-dimensional Kemmer equation in the presence of the Dirac oscillator potential. Following Greiner in [23], we have shown that the eigensolutions are decoupled in two sets.
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In this paper we use the so-called spinor-helicity formalism to represent three-vectors in terms of the Pauli matrices and derive a generalized relativistic wave equation for a massive fermion of spin one-half. We thus extend the ...
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In this paper we use the so-called spinor-helicity formalism to represent three-vectors in terms of the Pauli matrices and derive a generalized relativistic wave equation for a massive fermion of spin one-half. We thus extend the Dirac equation by making use of the Pauli-Lubariski operator that includes isospin explicitly. As a consequence, we get new degrees of freedom related to isospin helicity, in addition to the two standard ones of the Dirac equation that are associated with the kinetic spin-helicity doublet and the particle-antiparticle pair. Formally, isospin helicity has 2(2s + 1) degrees of freedom for an arbitrary general isospin s and has the eigenvalues s and - (s + 1), and thus it reveals a kind of hidden symmetry in any isospin field. The resulting four degrees of freedom for isospin 1/2 are interpreted as being associated with two independent subspaces of dimension 1 related to the U(1) and 3 related to SU(3) symmetry, i.e. to the leptons and quarks.
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The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The tw...
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The analytical expressions of the matrix elements for physical quantities are obtained for the Dirac oscillator in two and three spatial dimensions. Their behaviour for the case of operator's square is discussed in details. The two-dimensional Dirac oscillator has similar behavior to that for three-dimensional one.
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Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of t...
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Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth order for the remaining complex component. This equation is generally equivalent to the Dirac equation. Furthermore, following Schrodinger [Nature (London), 169, 538 (1952)], the remaining component can be made real by a gauge transform, thus extending to the Dirac field the Schrodinger conclusion that charged fields do not necessarily require complex representation. One of the two resulting real equations for the real function describes current conservation and can be obtained from the Maxwell equations in spinor electrodynamics (the Dirac-Maxwell electrodynamics). As the Dirac equation is one of the most fundamental equations, these results both belong in textbooks and can be used for development of new efficient methods and algorithms of quantum chemistry.
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We consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound state...
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We consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound states in Dirac materials, we study relativistic excitations with a position-dependent mass term. With the aid of an exactly-solvable model, we show how bound states begin to emerge after a critical condition on the size of the mass term is met. We also reveal some exotic properties of the unusual confinement discovered, including an elegant chevron structure of the bound state energies as a function of the size of the mass.
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The Einstein-Dirac equation is considered in the Robertson-Walker space-time. Solutions of the equation are looked for in the class of standard solutions of the Dirac equation. It is shown that the Einstein-Dirac equation does not...
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The Einstein-Dirac equation is considered in the Robertson-Walker space-time. Solutions of the equation are looked for in the class of standard solutions of the Dirac equation. It is shown that the Einstein-Dirac equation does not have standard solutions for both massive and massless Dirac field. Also superpositions of massive standard solutions are not solutions of the Einstein-Dirac equation. The result, that is briefly commented, is coherent and complementary to other existing results. Keywords Dirac equation - Einstein-Dirac equation - Robertson-Walker space-time - Solutions
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We construct a new discrete analogue of the Dirac-K?hler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-K?hler equation in the intrinsic notation as a set of di...
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We construct a new discrete analogue of the Dirac-K?hler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-K?hler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analogue of gauge transformations for the massless discrete Dirac-K?hler equations.
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We study the Dirac equation in the Kerr-Taub-NUT spacetime. We use Boyer-Lindquist coordinates and separate the resulting equations into radial and angular parts. We obtain some exact analytical solutions of the angular equations ...
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We study the Dirac equation in the Kerr-Taub-NUT spacetime. We use Boyer-Lindquist coordinates and separate the resulting equations into radial and angular parts. We obtain some exact analytical solutions of the angular equations for some special cases. We also obtain the radial wave equations with an effective potential. Finally, we discuss the potentials by plotting them as a function of radial distance in a physically acceptable region.
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We obtain a generalization of the nonrelativistic space-translation transformation to the Dirac equation in the case of a unidirectional laser pulse. This is achieved in a quantum-mechanical representation connected to the standar...
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We obtain a generalization of the nonrelativistic space-translation transformation to the Dirac equation in the case of a unidirectional laser pulse. This is achieved in a quantum-mechanical representation connected to the standard Dirac representation by a unitary operator T transforming the Foldy-Wouthuysen free-particle basis into the Volkov spinor basis. We show that a solution of the transformed Dirac equation containing initially low momenta p (p/mc << 1) will maintain this property at all times, no matter how intense the field or how rapidly it varies (within present experimental capabilities). As a consequence, the transformed four-component equation propagates independently electron and positron wave packets, and in fact the latter are propagated via two two-component Pauli equations, one for the electron, the other for the positron. These we shall denote as the Pauli low-momentum regime (LMR) equations, equivalent to the Dirac equation for the laser field. Successive levels of dynamical accuracy appear depending on how accurately the operator T is approximated. At the level of accuracy considered in this paper, the Pauli LMR equations contain no spin matrices and are in fact two-component Schrodinger equations containing generalized time-dependent potentials. The effects of spin are nevertheless included in the theory because, in the calculation of observables which are formulated in the laboratory frame, use is made of the spin-dependent transformation operator T. In addition, the nonrelativistic limit of our results reproduces known results for the laboratory frame with spin included. We show that in intense laser pulses the generalized potentials can undergo extreme distortion from their unperturbed form. The Pauli LMR equation for the electron is applicable to one-electron atoms of small nuclear charge (a Z 1) interacting with lasers of all intensities and frequencies co << mc~2.
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