A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles

TL;DR

This paper reviews the fermionic projector approach to quantum field theory, demonstrating how it models interacting Dirac particles, introduces a novel mass generation mechanism, and discusses causality-violating corrections.

Contribution

It presents a new formulation of quantum field theory using the fermionic projector, connecting it to standard results and revealing a novel boson mass generation mechanism.

Findings

Reproduces perturbative quantum field theory results

Introduces a new boson mass generation mechanism

Identifies small causality-violating corrections

Abstract

In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical system by a collection of Dirac states, including the states of the Dirac sea. Formulating the interaction by an action principle for the fermionic projector, we obtain a consistent description of interacting quantum fields which reproduces the results of perturbative quantum field theory. We find a new mechanism for the generation of boson masses and obtain small corrections to the field equations which violate causality.