Related papers: Notes on Factorization Algebras and TQFTs
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
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,…
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…
This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
We construct a certain `cobordism category' ${\cal D}$ whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
Recently, we introduced a new class of symmetry algebras, called satellite algebras, which connect with one another wavefunctions belonging to different potentials of a given family, and corresponding to different energy eigenvalues. Here…
We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…
This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can…
These notes are an extension of the rough notes provided for my four lecture graduate level course on "Quadratic Forms and Automorphic Forms" at the March 2009 Arizona Winter School on Quadratic Forms. They are meant to give a survey of…
Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…
In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…