Related papers: Flat Bundles on Function Manifolds and Evolution E…
We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives a new geometric point of view on these…
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
We perform an exact diagonalization study of the topological order in topological flat band models through calculating entanglement entropy and spectra of low energy states. We identify multiple independent minimal entangled states, which…
We study the equation E_fc of flat connections in a fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…
The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat…
We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is…
We construct an explicit bundle with flat connection on the configuration space of n points of a complex curve. This enables one to recover the `formality' isomorphism between the Lie algebra of the prounipotent completion of the pure braid…
We introduce the notion of a flat extension of a connection $\theta$ on a principal bundle. Roughly speaking, $\theta$ admits a flat extension if it arises as the pull-back of a component of a Maurer-Cartan form. For trivial bundles over…
We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a…
This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…
We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary,…
This paper is about algebro-geometrical structures on a moduli space $\CM$ of anomaly-free BV QFTs with finite number of inequivalent observables or in a finite superselection sector. We show that $\CM$ has the structure of F-manifold -- a…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…
We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of curves (conformal blocks) associated to modular fusion…
Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves are vector bundles. This relies on factorization, an…