Related papers: Quantum Topology Change in (2 + 1)d
The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
We investigate topology-changing processes in 4-dimensional quantum gravity with a negative cosmological constant. By playing the ``gluing-polytope game" in hyperbolic geometry, we explicitly construct an instanton-like solution without…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
The relativistic two-particle quantum mixtures are studied from the topological point of view. The mixture field variables can be transformed in such a way that a kinematical decoupling of both particle degrees of freedom takes place with a…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle-hole symmetry can open up new possibilities for topological phenomena in classical systems. Here…
We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and…
Phases of matter with non-trivial topological order are predicted to exhibit a variety of exotic phenomena, such as the existence robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant…
Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics more general than those of bosons or fermions. Such anyons emerge as quasiparticles in fractional quantum Hall states and certain frustrated…
The restriction of space-time dimensions to "2+1" leads us to a novel quantum field theory which has the Chern-Simons term in its action. This term changes the nature of gauge interaction by giving a so-called topological mass to a gauge…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
Holonomic phases---geometric and topological---have long been an intriguing aspect of physics. They are ubiquitous, ranging from observations in particle physics to applications in fault tolerant quantum computing. However, their…
Many years ago Friedman and Sorkin [1] established the existence of certain topological solitonic excitations in quantum gravity called (topological) geons. Geons can have quantum numbers like charge and can be tensorial or spinorial having…
Certain static soliton configurations of gauge fields in 4+1 dimensions correspond to the instanton in 4-Euclidean dimensions ``turned on its side,'' becoming a monopole in 4+1. The periodic instanton solution can be used with the method of…
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…