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.