Related papers: Topological mass mechanism and exact fields mappin…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
At small lattice spacing, or when using overlap fermions, lattice QCD simulations tend to become stuck in a single topological sector. Physical observables, e.g.\ hadron masses, then differ from their full QCD counterparts by $1/V$…
We investigate topological properties of density matrices motivated by the question to what extent phenomena like topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The…
Partially massless theory in three dimensions is revisited and its relationship with the self-dual massive gravity is considered. The only mode of the partially massless theory is shown explicitly through an action for a scalar field on…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…
Analysing a 3+1 dimensional model with four-Fermi interactions, we show that topological $\BF$ terms (both abelian and non-abelian) can be induced radiatively by massive fermions at the one-loop level. It is further pointed out that a…
A general definition of Chern-Simons actions in non-commutative geometry is proposed and illustrated in several examples. These are based on ``space-times'' which are products of even-dimensional, Riemannian spin manifolds by a discrete…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
The aim of this work is to proceed with the development of a model of topological electromagnetism in empty space, proposed by one of us some time ago and based on the existence of a topological structure associated with the radiation…
We show that various actions of topological conformal theories that were suggested recentely are particular cases of a general action. We prove the invariance of these models under transformations generated by nilpotent fermionic generators…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
The goal of the paper is to automatize the selection of mechanisms which are able to describe a set of measurements. In order to do so first we construct a set of possible mechanism fulfilling chemically reasonable requirements with a given…
We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction,…
We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering…
Exploring the synergy between topological physics and nonlinear dynamics unveils profound insights into emergent states of matter. Inspired by recent experimental demonstrations of topological frequency combs in photonics, we theoretically…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…
Choosing a suitable filtering function for the Mapper algorithm can be difficult due to its arbitrariness and domain-specific requirements. Finding a general filtering function that can be applied across domains is therefore of interest,…
By using the gauge-invariant but path-dependent, variables formalism, we consider a recently proposed topologically massive $U{\left( 1 \right)_{\cal W}} \times U{(1)_{\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In particular,…