Related papers: Introductory lectures on topological quantum field…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
(2+1) dimensional topological quantum field theories with defect excitations are by now quite well understood, while many questions are still open for (3+1) dimensional TQFTs. Here we propose a strategy to lift states and operators of a…
The object of this paper is to define a subcategory of the category of 3-cobordisms to which invariants of rational homology 3-spheres should generalize. We specify the notion of Topological Quantum Field Theory (in the sense of Atiyah) to…
In this paper we will analyse some interesting structures that occur in scalar quantum field theory. We will quantize this theory using path integrals. We will analyse the Bogomolny Bound for scalar quantum field theory in two dimensions.…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
For a positive integer r, an r-spin topological quantum field theory is a 2-dimensional TQFT with tangential structure given by the r-fold cover of SO_2 . In particular, such a TQFT assigns a scalar invariant to every closed r-spin surface…
This note is intended as an introduction to the functorial formulation of quantum field theories with defects. After some remarks about models in general dimension, we restrict ourselves to two dimensions - the lowest dimension in which…
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
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…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
This paper is a shortened version of the previous work hep-th/9907099: We propose a topological quantum field theory as a twisted candidate to formulate covariant matrix strings. The model relies on the octonionic or complexified instanton…
For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p.…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
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…
The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…
In this paper we discuss some questions about geometry over the field with one element, motivated by the properties of algebraic varieties that arise in perturbative quantum field theory. We follow the approach to F1-geometry based on…
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…