Related papers: Extended Structures in Topological Quantum Field T…
We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…
Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often extremely…
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications. One important problem asks for construction of a boundary-aligned frame field with prescribed singularity…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point functions and the lasso two-point functions are derived,…
We prove a decomposition formula for the dimensional reduction of an extended topological field theory that arises as an orbifold of an equivariant topological field theory. Our decomposition formula can be expressed in terms of a…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
New relations between algebraic geometry, information theory and Topological Field Theory are developed. One considers models of databases subject to noise i.e. probability distributions on finite sets, related to exponential families. We…
The realization of topological states of matter in ultracold atomic gases is currently the subject of intense experimental activity. Using a synthetic dimension, encoded in a non-spatial degree of freedom, can greatly simplify the…
We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
This article initiates the study of topological transcendental fields $\FF$ which are subfields of the topological field $\CC$ of all complex numbers such that $\FF$ consists of only rational numbers and a nonempty set of transcendental…
For vectors in $\mathbb{E}_3$ we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications. Based on properties of hyperbolic (Clifford)…
We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…
Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries,…
In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta…