Simplicial Quantum Gravity

• URL: http://arxiv.org/abs/2201.00226v2
• Date: Tue, 25 Jan 2022 22:07:04 GMT
• Title: Simplicial Quantum Gravity
• Authors: James B. Hartle
• Abstract summary: A four-dimensional simplicial geometry is made up of flat four-simplices joined together. A sum over simplicial geometries is a sum over thedifferent ways the simplices can be joined together with an integral over their edge lengths.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simplicial approximation and the ideas associated with the Regge calculus.provide a concrete way of implementing a sum over histories formulation ofquantum gravity. A four-dimensional simplicial geometry is made up of flat four-simplices joined together.A sum over simplicial geometries is a sum over thedifferent ways the simplices can be joined together with an integral over their edge lengths.Theconstruction of the simplicial Euclidean action for this approach to quantum general relativity is illustrated. The recovery of the diffeomorphism group in the continuum limit is discussed. Some possible classes of simplicial complexes with which to define a sum over topologies are described.

Related papers

• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies [1.3392361199400264]
  We show that the appropriate real-time path integral yields both R'enyi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail.
  arXiv  Detail & Related papers  (2024-09-25T23:32:49Z)
• Minimal Areas from Entangled Matrices [41.94295877935867]
  We show how entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula. Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.
  arXiv  Detail & Related papers  (2024-08-09T18:00:03Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Toward a physically motivated notion of Gaussian complexity geometry [0.0]
  We present a construction of a geometric notion of circuit complexity for Gaussian states. We show how to account for time-reversal symmetry breaking in measures of complexity. This establishes a first step towards building a quantitative, geometric notion of complexity.
  arXiv  Detail & Related papers  (2023-09-25T18:00:01Z)
• A new quantum computational set-up for algebraic topology via simplicial sets [0.0]
  A quantum computational framework for algebraic topology based on simplicial set theory is presented. The proposed set-up applies to any parafinite simplicial set and proceeds by associating with it a finite dimensional simplicial Hilbert space. A quantum algorithmic scheme capable to compute the simplicial homology spaces and Betti numbers of a simplicial set is outlined.
  arXiv  Detail & Related papers  (2023-09-20T13:30:43Z)
• Geometry Interaction Knowledge Graph Embeddings [153.69745042757066]
  We propose Geometry Interaction knowledge graph Embeddings (GIE), which learns spatial structures interactively between the Euclidean, hyperbolic and hyperspherical spaces. Our proposed GIE can capture a richer set of relational information, model key inference patterns, and enable expressive semantic matching across entities.
  arXiv  Detail & Related papers  (2022-06-24T08:33:43Z)
• Bounds on quantum evolution complexity via lattice cryptography [0.0]
  We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries.
  arXiv  Detail & Related papers  (2022-02-28T16:20:10Z)
• Dist2Cycle: A Simplicial Neural Network for Homology Localization [66.15805004725809]
  Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations. We propose a graph convolutional model for learning functions parametrized by the $k$-homological features of simplicial complexes.
  arXiv  Detail & Related papers  (2021-10-28T14:59:41Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Geometry of Complexity in Conformal Field Theory [0.0]
  We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories. We embed Fubini-Study state complexity and direct counting of stress tensor insertion in relevant circuits in a unified mathematical language.
  arXiv  Detail & Related papers  (2020-05-05T18:00:14Z)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

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.