Related papers: Higher Structures in Algebraic Quantum Field Theor…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are…
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
With this paper we hope to contribute to the theory of quantales and quantale-like structures. It considers the notion of $Q$-sup-algebra and shows a representation theorem for such structures generalizing the well-known representation…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…
I discuss effective field theories for heavy bound systems, particularly bound systems involving two heavy quarks. The emphasis is on the relevant concepts and on interesting physical applications and results.
In this letter we present some new results on modular theory and its application in quantum field theory. In doing this we develop some new proposals how to generalize concepts of geometrical action. Therefore the spirit of this letter is…
The notion of (symmetric) coloured operad or "multicategory" can be obtained from the notion of commutative algebra through a certain general process which we call "theorization" (where our term comes from an analogy with William Lawvere's…
There have been several attempts in recent years to extend the notions of symplectic and Poisson structures in order to create a suitable geometrical framework for classical field theories, trying to achieve a success similar to the use of…
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a…