Related papers: Quantum wormhole as a Ricci flow
The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical…
We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between…
We elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse-grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation,…
We show some relations between Ricci flow and quantum theory via Fisher information and the quantum potential.
We indicate some formulas connecting Ricci flow and the Perelman entropy functional to Fisher information, differential entropy, and the quantum potential.
A very simple wormhole geometry is considered as a model of a mode of topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of the hole reduces to quantum mechanics of one variable, throat radius, and admits a WKB…
In order to reconcile the wave-function collapse in quantum mechanics with the finiteness of signals' propagation in general relativity, we delve into a stochastic version of the Ricci flow and study its non-relativistic limit in presence…
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…
Quantization is performed of a Friedmann-Robertson-Walker universe filled with a conformally invariant scalar field and a perfect fluid with equation of state $p=\alpha \rho$. A well-known discrete set of static quantum wormholes is shown…
In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame (QSRF) is proposed.…
We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in…
We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and…
Spacetime undergoes quantum fluctuations, giving rise to spacetime foam, a.k.a. quantum foam. We discuss some properties of spacetime foam, and point out the conceptual interconnections in the physics of quantum foam, black holes, and…
A multidimensional cosmological model with space-time consisting of $n (n \ge 2)$ Einstein spaces $M_{i}$ is investigated in the presence of a cosmological constant $\Lambda$ and a homogeneous minimally coupled scalar field $\varphi(t)$ as…
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…
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 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)…
In this note we attempt to propose a categorical framework for the Ricci flow, treating it as a sequence of functors connecting the stack of Riemannian metrics to the category of geometric decompositions via singular flow spacetimes. To…
A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions,…
Free motion of a quantum particle with the wave function entirely comprised of plane waves with non-negative momenta may be accompanied by negative probability current, an effect called quantum backflow. The effect is weak and fragile, and…