Rockenbauer has further explained the relativistic Dirac
equation and how it gave a perfect description of the electromagnetic properties of an electron in his study.
are the 4 x 4 Dirac
[gamma]-matrices where [I.sub.2] and 0 are the 2 x 2 identity and null matrices respectively, and |[psi]> is the four component Dirac
[6,7] wave-function, h is the normalized Planck constant, c is the speed of light in vacuum, i = [square root of -1], and:
By comparing the second-order differential equation that has been obtained from Dirac
equation with Schrodinger equation for the well-known potential such as Scarff-II, Poshel-Teller, Morse, 3D-oscillator, and shift-oscillator potentials, the gauge field potential can be written based on the well-known superpotentials that are related to the mentioned potentials.
In the previous work , it was shown that D'Eath and Halliwell's  quantization of the Dirac
field in the closed FRW cosmology satisfies requirements similar to those just mentioned in the scalar field context; namely, the complex structure chosen in  is invariant under the symmetries of the field equations (which of course include SO(4), the isometry group of the spatial sections) and admits a unitary implementation of the dynamics.
Current [I.sub.DS] versus concentration of IgE is plotted at a constant gate voltage near the Dirac
The study showed how this naturally leads to the formation of stacked sets of topological surface states and 3D Dirac
fermions in the transition-metal dichalcogenides.
Soon after Dirac
presented his relativistic electron theory, (6,7) O.
The inverse problem and the spectral properties of Dirac
operators were investigated in detail by many authors [1, 2, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, 30, 31, 32].
In the wake of developments in science and technology, the (1 + 1)-dimensional nonlinear Dirac
(NLD) equations have emerged as useful models in many physical problems, such as Bose-Einstein condensates in honeycomb optical lattices  and the gap solitons in nonlinear optics .
 proposed a combination of the wavelet, DCT, and DIRAC
for EEG artifact removals, while their results could not tell how effective the method was in a qualitative manner.
One of the main aims of Clifford analysis is to study the function-theoretical properties of the null-solutions of the Dirac
operator which is invariant under rotations but not under reflections .
Addressing the needs of emergency and first responders, Lawrence Livermore National Laboratory and Dirac
Cuatro desarrollos teoricos que, a juicio de Colyvan, auspician el despliegue de (a) y (b), son: (i) la teoria de la gravitacion newtoniana, la cual, prima facie, caracteriza galaxias con cantidades inconsistentes de masa; (ii) la oceanografia descriptiva, que parece postular oceanos de profundidad finita e infinita; (iii) el calculo temprano, con sus cantidades infinitesimales fluctuantes; y (iv) la teoria cuantica de Dirac
, que incorpora una tecnica de normalizacion de vectores basada en la integracion de funciones inconsistentes.
Euclidean Clifford analysis offers a function theory with the Dirac
operator, which is an elegant generalization to higher dimensions of holomorphic functions in the complex plane.