Related papers: Module parallel transports in fuzzy gauge theory
Modular parallel transport is a generalization of Berry phases, applied to modular (entanglement) Hamiltonians. Here we initiate the study of modular parallel transport for disjoint field theory regions. We study modular parallel transport…
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional…
The motivation for this paper stems \cite{CR} from the need to construct explicit isomorphisms of (possibly nontrivial) principal $G$-bundles on the space of loops or, more generally, of paths in some manifold $M$, over which I consider a…
We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain…
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle…
Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This…
We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.
A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita…
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor…
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the…
We show that finite parallel transports of vectors in Riemannian spaces, determined by the multiplication law in the deformed groups of diffeomorphisms, and sequences of infinitesimal parallel transports of vectors along geodesics are…
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
We relate two different proposals to extend the \'etale topology into homotopy theory, namely via the notion of finite cover introduced by Mathew and via the notion of separable commutative algebra introduced by Balmer. We show that finite…
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…
We extend the usual notion of parallel transport along a path to triangulated surfaces. A homotopy of paths is lifted into a fibered category with connection and this defines a functor between the fibers above the boundary paths. These…
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed…
We introduce homotopy lattice gauge fields (HLGFs), a version of gauge fields over a discretized base, based on a notion of higher parallel transport that enriches the usual parallel transport along paths on a lattice to also consider…