# A gauge fixing procedure for causal fermion systems

@article{Finster2020AGF, title={A gauge fixing procedure for causal fermion systems}, author={Felix Finster and S. Kindermann}, journal={Journal of Mathematical Physics}, year={2020}, volume={61}, pages={082301} }

Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper, it is explained and worked out in detail that, despite this local gauge freedom, the structures of a causal fermion system give rise to distinguished gauges where the local gauge freedom is fixed completely up to global gauge transformations. The main method is to use spectral…

## 10 Citations

Banach manifold structure and infinite-dimensional analysis for causal fermion systems

- MathematicsAnnals of Global Analysis and Geometry
- 2021

A mathematical framework is developed for the analysis of causal fermion systems in the infinite-dimensional setting. It is shown that the regular spacetime point operators form a Banach manifold…

H\"older Continuity of the Integrated Causal Lagrangian in Minkowski Space

- Physics
- 2021

It is proven that the kernel of the fermionic projector of regularized Dirac sea vacua in Minkowski Space is L-integrable. The proof is carried out in the specific setting of a continuous…

A Positive Mass Theorem for Causal Fermion Systems

- Physics
- 2019

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat…

Numerical Analysis of the Causal Action Principle in Low Dimensions

- MathematicsArXiv
- 2022

This work provides a thorough numerical analysis of the causal action principle for weighted counting measures for large m in the cases n = 1, 2 and f = 2, 3, 4 and corroborate that all minimizers for largem are good approximations of the discrete Dirac spheres.

Elliptic methods for solving the linearized field equations of causal variational principles

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator…

A Positive Mass Theorem for Static Causal Fermion Systems

- Physics
- 2019

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat…

Two-dimensional area and matter flux in the theory of causal fermion systems

- Physics, Philosophy
- 2019

The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change…

Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

- PhysicsAnnales Henri Poincaré
- 2021

It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time t gives rise to a distinguished state on the algebra generated by…

Linear bosonic quantum field theories arising from causal variational principles

- PhysicsLetters in Mathematical Physics
- 2022

It is shown that the linearized fields of causal variational principles give rise to linear bosonic quantum field theories. The properties of these field theories are studied and compared with the…

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