Related papers: A Topological Phase in a Quantum Gravity Model
We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…
We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays…
Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of $B\w F$ theory. The extra symmetries not present in…
The bare bones of a theory of quantum gravity are exposed. It may have the potential to solve the cosmological constant problem. Less certain is its behavior in the Newtonian limit.
Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the…
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…
It is argued that (a) In the quantum realm test-particle masses have non-trivial observability which induces a non-geometric element in gravity, (b) Any theory of quantum gravity, on fundamental grounds, must contain an element of…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice…
A general introduction is given to what can be predicated about quantum gravity once the lessons from the standard model of particle physics are taken into account. In particular, the effective lagrangian point of view is briefly commented…
Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby…
In this work, we propose a topological quantum field theory phase for four-dimensional gravity. We show it is able to generate, not only General Relativity, but the whole family of Lovelock-Cartan theories of gravity. This is accomplished…
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and…
A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and…
I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
I discuss some aspects of a lattice approach to canonical quantum gravity in a connection formulation, discuss how it differs from the continuum construction, and compare the spectra of geometric operators - encoding information about…
Recently a new class of quantum phases of matter: symmetry protected topological states, such as topological insulators, attracted much attention. In presence of interactions, group cohomology provides a classification of these [X. Chen et…
A new approach is suggested which allows to describe phenomenologically arbitrary topologies of the Universe. It consists in a generalizaton of third quantization. This quantization is carried out for the case of asymptotic closeness to a…