Time evolution as refining, coarse graining and entangling

Abstract

We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.

35 pages, 8 figures; v2: explanations and references added, improved structure; v3 and v4: minor updates, accepted in New J. Phys

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• Emergence of Spacetime in a restricted Spin-foam model
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• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Projective Limits of State Spaces I. Classical Formalism
• On the fate of the Hoop Conjecture in quantum gravity
• From 3D topological quantum field theories to 4D models with defects
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• Holographic description of boundary gravitons in (3+1) dimensions
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• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Classification of constraints and degrees of freedom for quadratic discrete actions
• Perfect discretizations as a gateway to one-loop partition functions for 4D gravity
• A new realization of quantum geometry
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
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• Curvature effects in the spectral dimension of spin foams
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Is the local linearity of space-time inherited from the linearity of probabilities?
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• A Realist Interpretation of Unitarity in Quantum Gravity
• Knotted 4-regular graphs: polynomial invariants and the Pachner moves
• Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature
• Tensor networks for quantum causal histories