Causal Fermion Systems and the ETH Approach to Quantum Theory

• URL: http://arxiv.org/abs/2004.11785v2
• Date: Tue, 1 Sep 2020 14:30:18 GMT
• Title: Causal Fermion Systems and the ETH Approach to Quantum Theory
• Authors: Felix Finster, J\"urg Fr\"ohlich, Marco Oppio, Claudio F. Paganini
• Abstract summary: We review the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach) For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. We show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length.

Related papers

• Kubo-Martin-Schwinger relation for energy eigenstates of SU(2)-symmetric quantum many-body systems [41.94295877935867]
  We show that non-Abelian symmetries may alter conventional thermodynamics.<n>This work helps extend into nonequilibrium physics the effort to identify how non-Abelian symmetries may alter conventional thermodynamics.
  arXiv  Detail & Related papers  (2025-07-09T19:46:47Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction [2.9849762483081275]
  We extend previous analysis on decoherence in a fermion and scalar quantum field theory. We use a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. Our result is qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.
  arXiv  Detail & Related papers  (2023-07-25T12:14:19Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• Quantum Relativity of Subsystems [58.720142291102135]
  We show that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent.
  arXiv  Detail & Related papers  (2021-03-01T19:00:01Z)
• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems [0.0]
  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 fermionic and bosonic field operators.
  arXiv  Detail & Related papers  (2021-01-26T14:09:18Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Aspects of quantum information in finite density field theory [0.0]
  We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions.
  arXiv  Detail & Related papers  (2020-11-02T19:00:26Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Dynamics of Causal Fermion Systems. Field Equations and Correction Terms for a New Unified Physical Theory [0.0]
  We develop a formalism which connects the causal action principle to a suitable notion of fields on space-time. We find that the dynamics induced by the field equations conserve a symplectic form which gives rise to an Hamiltonian time evolution if the causal fermion system admits a notion of time.
  arXiv  Detail & Related papers  (2020-06-25T12:54:13Z)
• Generalized Entanglement, Charges and Intertwiners [0.0]
  We define a measure of entanglement entropy as a measure of information erased under restriction to a subspace of observables. We argue that the correct entanglement measure in the presence of charges is the sum of two terms; one measuring the entanglement of charge-neutral operators, and the other measuring the contribution of the bi-local intertwiners.
  arXiv  Detail & Related papers  (2020-05-22T20:49:05Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.