Causal fermion systems

Beyond the Standard Model
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The theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory.[1][2] Moreover, it gives quantum mechanics as a limiting case and has revealed close connections to quantum field theory.[3][4] Therefore, it is a candidate for a unified physical theory. Instead of introducing physical objects on a preexisting spacetime manifold, the general concept is to derive spacetime as well as all the objects therein as secondary objects from the structures of an underlying causal fermion system. This concept also makes it possible to generalize notions of differential geometry to the non-smooth setting.[5][6] In particular, one can describe situations when spacetime no longer has a manifold structure on the microscopic scale (like a spacetime lattice or other discrete or continuous structures on the Planck scale). As a result, the theory of causal fermion systems is a proposal for quantum geometry and an approach to quantum gravity.

Causal fermion systems were introduced by Felix Finster and collaborators.

  1. ^ Finster, Felix (2006). The Principle of the Fermionic Projector. Providence, R.I: American Mathematical Society. ISBN 978-0-8218-3974-4. OCLC 61211466.Chapters 1-4Chapters 5-8Appendices
  2. ^ Finster, Felix (2016). The Continuum Limit of Causal Fermion Systems. Fundamental Theories of Physics. Vol. 186. Cham: Springer International Publishing. arXiv:1605.04742. doi:10.1007/978-3-319-42067-7. ISBN 978-3-319-42066-0. ISSN 0168-1222. S2CID 119123208.
  3. ^ Finster, Felix (2014). "Perturbative quantum field theory in the framework of the fermionic projector". Journal of Mathematical Physics. 55 (4): 042301. arXiv:1310.4121. Bibcode:2014JMP....55d2301F. doi:10.1063/1.4871549. ISSN 0022-2488. S2CID 10515274.
  4. ^ Finster, Felix; Kamran, Niky (2021). "Complex structures on jet spaces and bosonic Fock space dynamics for causal variational principles". Pure and Applied Mathematics Quarterly. 17: 55–140. arXiv:1808.03177. doi:10.4310/PAMQ.2021.v17.n1.a3. S2CID 119602224.
  5. ^ Cite error: The named reference lqg was invoked but never defined (see the help page).
  6. ^ Finster, Felix; Kamran, Niky (2019). "Spinors on singular spaces and the topology of causal fermion systems". Memoirs of the American Mathematical Society. 259 (1251): v+83. arXiv:1403.7885. doi:10.1090/memo/1251. ISSN 0065-9266. S2CID 44295203.