On the Regularized Fermionic Projector of the Vacuum

Abstract

We construct families of fermionic projectors with spherically symmetric regularization, which satisfy the condition of a distributional $\mathcal{M}P$-product. The method is to analyze regularization tails with a power-law or logarithmic scaling in composite expressions in the fermionic projector. The resulting regularizations break the Lorentz symmetry and give rise to a multi-layer structure of the fermionic projector near the light cone. The remaining freedom for the regularization parameters and the consequences for the normalization of the fermionic states are discussed.

66 pages, LaTeX, 8 figures, minor improvements (published version)

References in corpus (6)

• A quantum field theory of simplicial geometry and the emergence of spacetime
• Fermion Systems in Discrete Space-Time - Outer Symmetries and Spontaneous Symmetry Breaking
• From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives
• An Action Principle for the Masses of Dirac Particles
• Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure
• Fermion Systems in Discrete Space-Time

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• Entanglement and Second Quantization in the Framework of the Fermionic Projector
• The Causal Action in Minkowski Space and Surface Layer Integrals
• An Action Principle for the Masses of Dirac Particles
• The Linear Dynamics of Wave Functions in Causal Fermion Systems
• Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems
• From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives
• Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Fermion Systems in Discrete Space-Time
• Modified Measures as an Effective Theory for Causal Fermion Systems
• On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space
• A Lattice Model for the Fermionic Projector in a Static and Isotropic Space-Time
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems