A Positive Mass Theorem for Static Causal Fermion Systems

Finster, Felix; Platzer, Andreas

doi:10.48550/arxiv.1912.12995

Cited by 5 publications

(20 citation statements)

References 32 publications

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“…In this way, we get into the setting of causal variational principles as introduced in Section 2.1. The resulting static κ-Lagrangian indeed has the properties (i)-(iv) in Section 2.1 (for details see [18,Section 3.3]).…”

Section: Example: Static Causal Fermion Systemsmentioning

confidence: 87%

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Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles

Finster,

Lottner

2021

Preprint

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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 which is shown to be bounded and symmetric on a Hilbert space endowed with a suitably adapted weighted L 2 -scalar product. Guided by the procedure in the theory of linear elliptic partial differential equations, we use the spectral calculus to define Sobolev-type Hilbert spaces and invert the linearized field operator as an operator between such function spaces. The uniqueness of the resulting weak solutions is analyzed. Our constructions are illustrated in simple explicit examples. The connection to the causal action principle for static causal fermion systems is explained.◮ Partial and jet derivatives with an index i ∈ {1, 2}, as for example in (2.14), only act on the respective variable of the function L. This implies, for example, that the derivatives commute,1 This assumption is convenient, because then the restricted EL equations (2.12) imply that ℓ vanishes identically on M .

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Section: Example: Static Causal Fermion Systemsmentioning

confidence: 87%

“…Static causal fermion systems were first considered in [18]. We here present a somewhat simpler setting where the constraints are built in right from the beginning.…”

Section: Example: Static Causal Fermion Systemsmentioning

confidence: 99%

Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles

Finster,

Lottner

2021

Preprint

Self Cite

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“…Therefore, we consider vector fields which are tangential to the hypersurfaces N t := T −1 (t). As shown in [29,Lemma 2.7], the divergence of such a vector field can be arranged to be any given function a ∈ C ∞ (M, R). Thus, by adding the corresponding inner solutions we can achieve that all linearized solutions have no scalar components.…”

Section: ˆR3mentioning

confidence: 99%

Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals

Finster¹,

Kamran²,

Reintjes³

2022

Preprint

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This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various integrands with a specific scaling behavior in this dimension. It is shown that, in a well-defined limiting case, the localized refined pre-state is positive and allows for the description of general entangled states.

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“…Static causal fermion systems were first considered in [16]. We here present a somewhat simpler setting where the constraints are built in right from the beginning.…”

Section: Example: Static Causal Fermion Systemsmentioning

confidence: 99%

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

Finster

Magdalena

2022

Calc. Var.

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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 which is shown to be bounded and symmetric on a Hilbert space endowed with a suitably adapted weighted $$L^2$$ L 2 -scalar product. Guided by the procedure in the theory of linear elliptic partial differential equations, we use the spectral calculus to define Sobolev-type Hilbert spaces and invert the linearized field operator as an operator between such function spaces. The uniqueness of the resulting weak solutions is analyzed. Our constructions are illustrated in simple explicit examples. The connection to the causal action principle for static causal fermion systems is explained.

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A Positive Mass Theorem for Static Causal Fermion Systems

Cited by 5 publications

References 32 publications

Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles

Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles

Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals

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

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