Related papers: A Topological Phase in a Quantum Gravity Model
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.
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…
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…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
What can we learn about quantum gravity from a simple toy model, without actually quantizing it? The toy model consists of a finite number of point particles, coupled to three dimensional Einstein gravity. It has finitely many physical…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…
What are topological phases of matter? First, they are phases of matter at zero temperature. Second, they have a non-zero energy gap for the excitations above the ground state. Third, they are disordered liquids that seem have no feature.…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
We describe a simple lattice model of higher-curvature quantum gravity in two dimensions and study the phase structure of the theory as a function of the curvature coupling. It is shown that the ensemble of flat graphs is entropically…
In this work, we present a theory for topological phases for quantum systems on tree graphs. Conventionally, topological phases of matter have been studied in regular lattices, but also in quasicrystals and amorphous settings. We consider…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…
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…
I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple…
(2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian Chern-Simons gauge field theory (E Witten 1988). Regarding this as the topological phase of quantum gravity in (2+1)d, we suggest a topological symmetry breaking by…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…