Related papers: Ricci Flow Approach to The Cosmological Constant P…
A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local…
In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature. As a step towards resolving the problem of time in quantum gravity, we attempt to merge the Ricci…
This paper is a generalization of earlier papers [Nucl. Phys. B 884, 344 (2014) (arXiv:1312.2759) and JHEP 6, 63 (2015) (arXiv:1401.2488)]. We generalize the idea of quantum clock time to quantum spacetime reference frame via physical…
The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential…
Recently, a new cosmological framework, dubbed Ricci Cosmology, has been proposed. Such a framework has emerged from the study of relativistic dynamics of fluids out of equilibrium in a curved background and is characterised by the presence…
Quantum treatment of physical reference frame leads to the Ricci flow of quantum spacetime, which is a quite rigid framework to quantum and renormalization effect of gravity. The theory has a low characteristic energy scale described by a…
Ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes. This idea has been around…
We revisit spatially flat FLRW cosmology in light of recent advances in standard model relativistic fluid dynamics. Modern fluid dynamics requires the presence of curvature-matter terms in the energy-momentum tensor for consistency. These…
It is known that the conformal instability or bottomless problem rises in the path integral method in quantizing the general relativity. Does quantum spacetime itself really suffer from such conformal instability? If so, does the conformal…
The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincar\'e Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first…
We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum)…
The paper proposes a statistical fields theory of quantum reference frame underlying the Perelman's analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a d=4-{\epsilon} quantum non-linear sigma…
The two-dimensional renormalization group acting as the Ricci flow $\Lambda\frac{\partial}{\partial\Lambda} g_{\mu\nu} = R_{\mu\nu}$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts…
We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow on Riemannian manifolds. First we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only…
We follow a new pathway to the definition of the Stochastic Quantization (SQ), first proposed by Parisi and Wu, of the action functional yielding the Einstein equations. Hinging on the functional similarities between the Ricci-Flow equation…
General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily…
It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $\Lambda$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical…
We find the regime of our recently constructed topological nonrelativistic quantum gravity, in which Perelman's Ricci flow equations on Riemannian manifolds appear precisely as the localization equations in the path integral. In this…
We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore links with the recently discussed…
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by…