相关论文: Gravity model for topological features on a cylind…

We define a new geometric flow, which we shall call the $K$-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston's model geometries under this flow both analytically and numerically. As an example, we show that an…

The main object of the proposed theory is not a pseudometric, but a symmetric affine connection on the Minkowski space. The coefficients of this connection have one upper and two lower indices. These coefficients are symmetric with respect…

We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a…

Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…

Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…

Gravity theory is the basis of modern cosmological models. Thirring-Feynman's tensor field approach to gravitation is an alternative to General Relativity (GR). Though Field Gravity (FG) approach is still developing subject, it opens new…

We propose a mathematically concrete way of modelling the suggestion that in quantum gravity the spacetime disappears, replacing it with a discrete approximation to the causal path space described as an object in a model category. One of…

A topological theory for the interactions in Nature is presented. The theory derives from the cyclic properties of the topological manifold Q=2T^3 + 3S^1 x S^2 which has 23 intrinsic degrees of freedom, discrete Z_3 and Z_2 x Z_3 internal…

We give a review of recent work aimed at understanding the dynamics of gravitational collapse in quantum gravity. Its goal is to provide a non-perturbative computational framework for understanding the emergence of the semi-classical…

The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…

This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…

The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…

A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…

We propose the theory of quantum gravity with interactions introduced by topological principle. The fundamental property of such a theory is that its energy-momentum tensor is an BRST anticommutator. Physical states are elements of BRST…

The partition function of 2+1 Chern-Simons Witten topological gravity has an attractive interpretation in terms of the unbroken and broken phases of gravity. We make this physical interpretation manifest using the background field method.

The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of…

We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we…

Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…

This paper discusses the somewhat unintuitive conjecture that many Lorentz-invariant many-particle models can be reinterpreted to satisfy the gtr field equations. It is shown that a careful remapping of coordinates yields a non-trivial…

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…