Related papers: Quantum Field Theories on Algebraic Curves
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
In this letter we develope an operator formalism for the $b-c$ systems with conformal weight $\lambda=1$ defined on a general closed and orientable Riemann surface. The advantage of our approach is that the Riemann surface is represented as…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
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…
In this work, the following conjectures are proven in the case of a Riemann surface with abelian group of symmetry: a) The $b-c$ systems on a Riemann surface $M$ are equivalent to a multivalued field theory on the complex plane if $M$ is…
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.
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We present new constructions of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) codes from algebraic curves. Unlike previous approaches based on elliptic curves, our method applies to curves that are Kummer extensions of the rational…
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…
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 provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, a…
We provide a short introduction to the main features of the algebraic approach to quantum field theories.
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
In this paper we try to prepare a framework for field quantization. To this end, we aim to replace the field of scalars R by self-adjoint elements of a commutative C-algebra, and reach an appropriate generalization of geometrical concepts…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
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…