Related papers: Topological quantum field theories
We provide a short and non-technical summary of our current knowledge and some possible perspectives on the group field theory formalism for quantum gravity, in the form of a (partial) FAQ (with answers). Some of the questions and answers…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple…
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordstr\"om, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…
The gauge field theories are usually quantized by fixing gauge. In this paper, we propose a new formalism that quantizes gauge fields without gauge fixing but naturally follows canonical formalism. New physical implications will follow.
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Tame geometry originated in mathematical logic and implements strong finiteness properties by defining the notion of tame sets and functions. In part I we argued that observables in a wide class of quantum field theories are tame functions…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
This is a translation into English of my Masters thesis (hovedoppgave) from 1991. The main topic of the thesis is the relation between fundamental physics and philosophy, and a discussion of several possible ontologies of quantum field…
Motivated by the question of exploring the "theory space" of quantum field theories, we review the concept of "decomposing" and "gluing" quantum field theories. We explain this in the context of three-dimensional $\mathcal{N}=2$…
This work deals with scalar field theories and supersymmetric quantum mechanics. The investigation is inspired by a recent result, which shows how to use the reconstruction mechanism to describe two distinct field theories from the very…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.