Dirac equation

Dirac equation is one of formulations of relativistic quantum mechanics. The Dirac equation is perhaps the most powerful equation of modern physics. It has wide range of applications and uses. The most important prediction was that of anti-particle.

There are several obvious dominance of the dirac equation in comparison to its nonrelativistic counterpart, Schrödinger equation (or the Pauli equation for particles with spin 1/2). First of all, the Dirac equation is compatible with the special theory of relativity, because the proper orthochronous Poincaré group has a representation by symmetry transformations in the state space associated with the Dirac equation.

On the other hand, the Dirac equation shows some strange effects. It modifies relativistic kinematics in a quite unexpected way through the appearance of negative energies (or negative masses). The energy according to the Dirac equation is not bounded from below (>=). This causes the usual free variational methods for computing energy eigenvalues to fail. Therefore one might think of considering replacements of the Dirac equation by equations with energy bounded from below. The principle The energy- momentum equation describes how mass is altered as the velocity of a body increases. There are two kinds of masses: one is proper mass and other is relativistic mass. Proper mass is the mass which is measured in the rest frame of the material body. As the velocity of the body increases, the kinetic energy is added as extra mass. The change of kinetic energy is the same as change of mass so that the relativistic energy relation reduces to classical energy conservation law in low velocity limit.

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