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

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.

16 pages, LaTeX, 1 figure, minor changes (published version)

References in corpus (3)

• A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
• Time Evolution of the External Field Problem in QED
• Renormalization and asymptotic expansion of Dirac's polarized vacuum

Cited by in corpus (12)

• "Vacuum-like" Hadamard states for quantum fields on curved spacetimes
• Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• Causal Fermion Systems: A Primer for Lorentzian Geometers
• Perturbative Quantum Field Theory in the Framework of the Fermionic Projector
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
• Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
• Spinors on Singular Spaces and the Topology of Causal Fermion Systems
• A Mechanism of Baryogenesis for Causal Fermion Systems
• Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ${\varphi }^4$-Theory
• Local Algebras for Causal Fermion Systems in Minkowski Space
• The Dirac Sea for the Non-Separable Hilbert Spaces