Related papers: Introduction to topological symmetry in QFT

We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is…

We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This…

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…

In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.

The Bott index has become an indispensable tool to probe the topology of quantum matter, particularly in systems lacking translational symmetry. Constructed from a plaquette operator, it retains the phase information while discarding the…

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a…

A particular approach to topology change in quantum gravity is reviewed, showing that several aspects of Stephen's work are intertwined with it in an essential way. Speculations are made on possible implications for the causal set approach…

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

The idea of a sutured topological quantum field theory was introduced by Honda, Kazez and Mati\'c (2008). A sutured TQFT associates a group to each sutured surface and an element of this group to each dividing set on this surface. The…

This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…

We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

I describe a project to open a new territory of quantum field theory where the fields live not on a space-time manifold but on certain complete metric spaces of (n-1)-dimensional objects (defects) in a 2n-dimensional space-time M. These…

It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…

We present the proper co-frame and its corresponding (diagonal) co-frame/spin connection pair for spherically symmetric geometries which can be used as an initial ansatz in any theory of teleparallel gravity. The Lorentz transformation…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…