Related papers: Quantum Topology Change in (2 + 1)d
We consider the quantization of space-times which can possess different topologies within a symmetry reduced version of Wheeler-DeWitt theory. The quantum states are defined from a natural decomposition as an outer-product of a topological…
Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on…
Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…
Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…
The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it…
Three-dimensional (3D) topological materials exhibit much richer phenomena than their lower-dimensional counterparts. Here, we propose self-localized topological states (i.e., topological solitons) in a 3D nonlinear photonic Chern…
We explore the space of solutions of the classical equations of motion in the Euclidean electroweak theory. We sketch a topological prescription that finds known solutions and indicates the existence of novel ones. All spatially-varying,…
We present a review of the spin and statistics of topological geons, particles in 3+1 quantum gravity. They can have half-odd-integral spin and fermionic statistics and since the underlying gravitational field is tensorial and bosonic, this…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
We analyze the edge mode structure of Euclidean three dimensional gravity from within the quantum theory as embodied by a Ponzano-Regge-Turaev-Viro discrete state sum with Gibbons-=-Hawking-York boundary conditions. This structure is…
We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer…
In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that…
Two-time physics (2T) is a general reformulation of one-time physics (1T) that displays previously unnoticed hidden symmetries in 1T dynamical systems and establishes previously unknown duality type relations among them. This may play a…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…