Related papers: Categorification of algebraic quantum field theori…

Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of…

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…

We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type $A_n$. These 2-representations naturally extend the right-multiplication 2-representation of…

We show that reasonably well behaved 3d and 4D TQFts must contain certain algebraic structures. In 4D, we find both Hopf categories and trialgebras.

We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying…

We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.

This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…

In this article, which builds upon the work done in our previous paper, the chiral aspects of 2dcft on globally hyperbolic Lorentzian manifolds are developed and explored within the perturbative algebraic quantum field theory (pAQFT)…

We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…

Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…

Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…

Using methods coming from non-formal equivariant quantization, we construct in this short note a unitary dual 2-cocycle on a discrete family of quotient groups of subgroups of the affine group of a local field (which is not of…

To each local field (including the real or complex numbers) we associate a quantum dilogarithm and show that it satisfies a pentagon identity and some symmetries. Using an angled version of these quantum dilogarithms, we construct three…

We categorify Lusztig's version of the quantized enveloping algebra for sl(2). Using a graphical calculus a 2-category is constructed whose split Grothendieck ring is isomorphic to Lusztig's algebra. The indecomposable morphisms of this…

Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. Nowdays many examples of symmetries of…

I describe how integrable quantum field theories in 2 spacetime dimensions are characterized by infinite dimensional quantum group symmetries, namely the q-deformations of affine Lie algebras, and their Yangian limit. These symmetries can…

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,…

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…