Introductory review on quantum field theory with space–time resolution

Abstract

We review the steps needed to reduce quantum field theory to quantum mechanics as its limiting case. While processes involving a changing number of particles require a quantum field theoretical description, some works used quantum mechanical data based on the single particle Dirac equation to predict the outcome. These non-quantum field theoretical approaches have led to conceptual controversies that are often related to the negative energy states, which are characteristic of the Dirac equation. As a result, the issues about the physical reality of the relativistic localisation phenomenon, the Zitterbewegung and the Klein paradox are widely discussed in many textbooks. In order to contribute to this discussion, we review recent computer simulations of oversimplified model systems based on quantum field theory. The direct visualisation of intrinsically quantum field theoretical process with full spatial and temporal resolutions can provide us with some first insight into the spontaneous electron–positron pair creation from the vacuum triggered by a strong external (supercritical) force field and with the resolution of the Klein paradox.