The Theory of Causal Fermion Systems

Introduction for Mathematicians

Introduction for mathematicians

It is a basic concept in the theory of Causal Fermion Systems that all the space-time structures (geometry, topology, fields, wave functions, etc.) are encoded in linear operators on a Hilbert space. More precisely, every space-time point corresponds to one operator. The relations between different space-time points are encoded in the corresponding operator products. The physical equations are formulated via a nonlinear variational principle, the causal action principle.

Causal fermion systems use methods of and give close connections to the following areas of mathematics:

  • functional analysis
  • measure theory
  • calculus of variations
  • Lorentzian geometry
  • Hyperbolic partial differential equations
  • Fourier analysis and microlocal analysis
  • Methods of quantum field theory: Fock spaces, Feynman diagrams, renormalization
  • Methods of non-smooth and infinite-dimensional analysis.

→  overview of the fundamental mathematical structures
→  basic definitions

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