An Action Principle for an Interacting Fermion System and its Analysis in the Continuum Limit

Abstract

We introduce and analyze a system of relativistic fermions in a space-time continuum, which interact via an action principle as previously considered in a discrete space-time. The model is defined by specifying the vacuum as a sum of Dirac seas corresponding to several generations of elementary particles. The only free parameters entering the model are the fermion masses. We find dynamical field equations if and only if the number of generations equals three. In this case, the dynamics is described by a massive axial potential coupled to the Dirac spinors. The coupling constant and the rest mass of the axial field depend on the regularization; for a given regularization method they can be computed as functions of the fermion masses. The bosonic mass term arises as a consequence of a symmetry breaking effect, giving an alternative to the Higgs mechanism. In addition to the standard loop corrections of quantum field theory, we find new types of correction terms to the field equations which violate causality. These non-causal corrections are too small for giving obvious contradictions to physical observations, but they might open the possibility to test the approach in future experiments.

incorporated in monograph arXiv:1605.04742 [math-ph] as Chapter 3

Cited by in corpus (7)

• A Lorentzian Quantum Geometry
• Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
• On the Support of Minimizers of Causal Variational Principles
• On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
• Perturbative Quantum Field Theory in the Framework of the Fermionic Projector
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
• Entanglement and Second Quantization in the Framework of the Fermionic Projector