相关论文: A Topos Model for Loop Quantum Gravity
This is a review article on quantum gravity. In section 1, the Penrose singularity theorem is proven. In section 2, the covariant quantization approach of gravity is reviewed. In section 3, an article by Hawking is reviewed that shows the…
Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke. In the monoidal…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational…
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
We investigate the action of diffeomorphisms in the context of Hamiltonian Gravity. By considering how the diffeomorphism-invariant Hilbert space of Loop Quantum Gravity should be constructed, we formulate a physical principle by demanding,…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
One of the major issues confronting theoretical physics is finding a quantum theory of gravity and a resolution to the cosmological constant problem. It is believed that a true quantum theory of gravity will lead to a solution to the this…
With a well-motivated extension of higher order holonomy corrections, the quantum theory of loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model (with a free massless scalar) is rigorously formulated. The analytical…
In the foundational logical framework of homotopy-type theory we discuss a natural formalization of secondary integral transforms in stable geometric homotopy theory. We observe that this yields a process of non-perturbative cohomological…
Loop Quantum Cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer remedy or modify various classical cosmology aspects. In this paper we address the…
The collapse of a spherically symmetric ball of dust has been intensively studied in Loop Quantum Gravity (LQG). From a quantum theory, it is possible to recover a semiclassical regime through a polymerization procedure. In this setting,…
It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Topos quantum mechanics, developed by Isham et. al., creates a topos of presheaves over the poset V(N) of abelian von Neumann subalgebras of the von Neumann algebra N of bounded operators associated to a physical system, and established…
Projective structures have successfully been used for the construction of measures in the framework of loop quantum gravity. In the present paper, we establish such structures for the configuration space $\mathbb{R}\sqcup…
Building on prior work, a generally covariant reformulation of free scalar field theory on the flat Lorentzian cylinder is quantized using Loop Quantum Gravity (LQG) type `polymer' representations. This quantization of the {\em continuum}…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics $e^{\phi(z)}dz^2$, conjecturally describing scaling limits of discrete $2d$-random surfaces. The law of the random field $\phi$ in LQFT depends on…
Spinfoams provide a framework for the dynamics of loop quantum gravity that is manifestly covariant under the full four-dimensional diffeomorphism symmetry group of general relativity. In this way they complete the ideal of…