Noether-Like Theorems for Causal Variational Principles

Abstract

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is proven that these symmetries give rise to corresponding conserved quantities, expressed in terms of so-called surface layer integrals. In a suitable limiting case, the Noether-like theorems for causal fermion systems reproduce charge conservation and the conservation of energy and momentum in Minkowski space. Thus the conservation of charge and energy-momentum are found to be special cases of general conservation laws which are intrinsic to causal fermion systems.

41 pages, LaTeX, 3 figures, small improvements (published version)

References in corpus (4)

• The Continuum Limit of Causal Fermion Systems
• Perturbative Quantum Field Theory in the Framework of the Fermionic Projector
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
• The Fermionic Projector, Entanglement, and the Collapse of the Wave Function

Cited by in corpus (20)

• A Hamiltonian Formulation of Causal Variational Principles
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principles
• The Causal Action in Minkowski Space and Surface Layer Integrals
• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
• Spinors on Singular Spaces and the Topology of Causal Fermion Systems
• Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems
• The Linear Dynamics of Wave Functions in Causal Fermion Systems
• A Mechanism of Baryogenesis for Causal Fermion Systems
• Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed
• A Class of Conserved Surface Layer Integrals for Causal Variational Principles
• Positive Functionals Induced by Minimizers of Causal Variational Principles
• Causal Fermion Systems: Classical Gravity and Beyond
• Construction of Global Solutions to the Linearized Field Equations for Causal Variational Principles
• Dynamical Gravitational Coupling as a Modified Theory of General Relativity
• A Positive Mass Theorem for Static Causal Fermion Systems
• Causal Fermion Systems as an Effective Collapse Theory
• A Notion of Entropy for Causal Fermion Systems
• Notions of Fermionic Entropies of a Causal Fermion System
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems