# A generalized time-dependent relativistic wave equation

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In a Riemannâ€“Cartan space-time U4 the minimally coupled massive spin-S Dirac equations are subject to constraints for all S> 1/2 . One may seek to modify these equations by the inclusion of appropriate supplementary terms Î±, Î² (indices suppressed) in such a way that the modified...

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The solution of the Dirac equation in the wave package form in a slightly curved spacetime (compared with the size of the wave package) was studied. For the metric in the Kerr-Schield form, a system of common differential equations describing spin conditions of massive neutral Dirac particles...

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In previous work, Diracâ€™s constraint mechanics and supersymmetry were used to construct two-body Dirac equations for particles interacting through world scalar and vector potentials. The resulting compatible 16-component wave equations, S1Ïˆ=Î³51(Î³1Â·(p1-A1) +m1+S1)Ïˆ=0,...

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With the help of perturbation theory the asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem in 2+1 dimensions are obtained. We compare the results obtained with the data from similar approximation for...

- Matrix-Differential-Operator Approach toÂ theÂ MaxwellÂ Equations and the Dirac Equation. Xiaoping Xu // Acta Applicandae Mathematica;Jul2008, Vol. 102 Issue 2/3, p237
AbstractÂ Â We use matrix-differential-operators and Fourier expansion to solve the Maxwell equations and the free Dirac equation for any given initial conditions.

- ON THE DIRAC EQUATION IN CURVED SPACE-TIME. POLLOCK, M. D. // Acta Physica Polonica B;Aug2010, Vol. 41 Issue 8, p1827
We discuss in detail the general-relativistically covariant Dirac equation derived by Fock for a particle of rest mass m and charge e in an electromagnetic potential Ai, [iÎ³k(âˆ‚k - Î“k - ieAk) m]Î¨ = 0. The spinorial affine connection is given in terms of the spin connection...

- Plasma excitations of dressed Dirac electrons in graphene layers. Roslyak, Oleksiy; Gumbs, Godfrey; Huang, Danhong // Journal of Applied Physics;Jun2011, Vol. 109 Issue 11, p113721
Collective plasma excitations of optically dressed Dirac electrons in single and double graphene layers are calculated in the RPA. The presence of circularly polarized light gives rise to an energy gap Eg between the conduction and valence energy bands. Its value may be adjusted by varying the...

- Noncommutative Integration of the Dirac Equation in a Flat Space and in the de Sitter Space. Tyumentsev, V. A.; Klishevich, V. V. // Russian Physics Journal;Sep2003, Vol. 46 Issue 9, p891
Noncommutative integration of the Dirac massive and massless equations is performed in a four-dimensional flat space and in the de Sitter space of arbitrary signature. A new class of rigorous solutions of the Dirac equation is constructed in these spaces. The properties of the solutions obtained...

- Rotational modes in a phononic crystal with fermion-like behavior. Deymier, P. A.; Runge, K.; Swinteck, N.; Muralidharan, K. // Journal of Applied Physics;2014, Vol. 115 Issue 16, p163510-1
The calculated band structure of a two-dimensional phononic crystal composed of stiff polymer inclusions in a soft elastomer matrix is shown to support rotational modes. Numerical calculations of the displacement vector field demonstrate the existence of modes whereby the inclusions and the...