Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 26

We begin this chapter by obtaining the relativistic “Schroödinger” equation for a free spin-1/2 field by following first the historical approach, and then presenting a derivation based on Lorentz covariance and space-time parity alone. This leads us to a four-component wave equation which is first-order in space and time coordinates. We present the solution of this equation for three choices of basis: The Dirac, Weyl (or chiral), and Majorana representations. The latter representation is shown to be particularly useful for the case of Majorana fermions, i.e. fermions which are their own anti-particles. We show that the Dirac equation allows for the notion of a probability density after suitable interpretation of the negative energy states.