Related papers: An Operator-Algebraic Framework for Anyons and Def…
We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with…
The Doplicher-Haag-Roberts (DHR) reconstruction theorem shows that standard ($0$-form) internal symmetries are associated to groups in relativistic quantum field theory in spacetime dimension $D>2$. In particular, non-invertible symmetry…
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For…
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…
We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
For any finite-dimensional algebra $A$ over a field $k$ with finite global dimension, we investigate the root category $\cR_A$ as the triangulated hull of the 2-periodic orbit category of $A$ via the construction of B. Keller in "On…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We establish a rigorous link between infinite-dimensional regular Fr\"olicher Lie groups built out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We introduce a version of the Kadomtsev-Petviashvili…
We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
We present a unified category-theoretic framework for quantum Hall hierarchy constructions and anyon superconductivity based on modular tensor categories over $\mathrm{Rep}(\mathrm{U}(1))$ and $\mathrm{sRep}(\mathrm{U}(1)^f)$. Our approach…
We consider the construction of integrable quantum field theories in the operator-algebraic approach, which is based on quantum fields localized in infinitely extended wedge regions. This approach has been successful for the construction of…
In this paper, we extend past work done on the application of the mathematics of category theory to quantum information science. Specifically, we present a realization of a dagger-compact category that can model finite-dimensional quantum…
We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion…
We propose a class of pure states of two-dimensional lattice systems realizing topological order associated with unitary rational vertex operator algebras. We show that the states are well-defined in the thermodynamic limit and have…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is…