Unitary and nonunitary approaches in quantum field theory

Abstract

We use a simplified essential state model to compare two quantum field theoretical approaches to study the creation of electron-positron pairs from the vacuum. In the unitary approach the system is characterized by a state with different numbers of particles that is described by occupation numbers and evolves with conserved norm. The nonunitary approach can predict the evolution of wave functions and density operators with a fixed number of particles but time-dependent norms. As an example to illustrate the differences between both approaches, we examine the degree of entanglement for the Klein paradox, which describes the creation of an electron-positron pair from vacuum in the presence of an initial electron. We demonstrate how the Pauli blocking by the initial electron comes at the expense of a gain in entanglement of this electron with the created electron as well as with the created positron.