The factor 1/2 [??] in [S.sub.i] implies that the

Dirac particle carries spin 1/2, hence, the Dirac equation (1) is an equation for a particle with spin 1/2!

For a

Dirac particle on a one-dimensional ring whose energy is given by (5), the persistent current is

First considered by the German mathematician, mathematical physicist and philosopher--Hermann Klaus Hugo Weyl (1885-1955); a massless

Dirac particle is described by the following Dirac-Weyl [13] equation:

Yang, "Seiberg-Witten map and quantum-phase effects for neutral

Dirac particle on noncommutative plane," Physics Letters B, vol.

Subsequently, using the modified Dirac equation, we calculate the tunneling probability of the

Dirac particle by using the Hamilton-Jacobi method, and, then, we find the modified Hawking temperature of the black hole.

Yang, "Seiberg-Witten map and quantum phase effects for neutral

Dirac particle on noncommutative plane," Physics Letters B, vol.

As the Dirac theory has a vacuum including Zitterbewegung oscillations between positive and negative energy states and perfectly explains an interaction of a

Dirac particle with an atomic structure of the materials, it gives a reasonable cosmological solutions for the early-time inflation and late-time acceleration of the universe [35].

By applying L'Hospital rule near the black hole event horizon, the surface gravity due to

Dirac particle is given by

We will establish a lagrangian that gives

Dirac particle motion in the flat space limit, electromagnetism and a form for GR that gives a simple parallel between the motion of the gravitational fields, [[gamma].sub.v] and the electromagnetic ones Av that allows gravity to obtain the nonlinear "geometric" features of GR.

where the final (-[e.sub.*]) in (7) and (8) refers to the Planck particles at a radius r from the stationary

Dirac particle at r = 0.

Goldhaber, "

Dirac particle in a magnetic field: symmetries and their breaking by monopole singularities," Physical Review D, vol.

Thus these coupling forces do not lead to a

Dirac particle in the positron and proton cases--nor can they produce their corresponding Compton radii [r.sub.c] = [e.sup.2.sub.*]/[mc.sup.2] from (3), where F([r.sub.c]) must vanish.