Related papers: Higher Structures in Algebraic Quantum Field Theor…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
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 give an account of the current state of the approch to quantum field theory via Hopf algebras and Hochschild cohomology. We emphasize the versatility and mathematical foundation of this algebraic structure, and collect algebraic…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools…
We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field…
In this talk the main features of the operator formalism for the $b-c$ systems on general algebraic curves developed in refs. [1-2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure…