The Dirac Equation in Geometric Quantization

Quantization for a Nonlinear Dirac Equation

We study solutions of certain nonlinear Dirac-type equations on Riemann spin surfaces. We first improve an energy identity theorem for a sequence of such solutions with uniformly bounded energy in the case of a fixed domain. Then, we prove the corresponding energy identity in the case that the equations have constant coefficients and the domains possibly degenerate to a spin surface with only N...

Quantization of Dirac Field

On the Dirac Equation in a Gravitation Field and the Secondary Quantization

The Dirac equation for massive free electrically neutral spin 1/2 particles in a gravitation field is considered. The secondary quantization procedure is applied to it and the Hilbert space of multiparticle quantum states is constructed. 1. The Dirac equation and its current. Let M be a space-time manifold. It is a four-dimensional orientable manifold equipped with a pseudo-EuclideanMinkowski-t...

Decoherence in the Dirac Equation

A Dirac particle is represented by a unitarily evolving state vector in a Hilbert space which factors as Hspin Hposition. Motivated by the similarity to simple models of decoherence consisting of a two state system coupled to an environment, we investigate the occurence of decoherence in the Dirac equation upon tracing over position. We conclude that the physics of this mathematically exact mod...

The Modified Dirac Equation

We consider the behavior of particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle’s Compton wavelength. For higher energies however, both the Klein-Gordon and Dirac equations get modified and this leads to some new effects for the particles, including the appearan...