Related papers: Topological sectors for Weyl-algebra net in the Ei…
This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool.…
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…
One of the themes in algebraic geometry is the study of the relation between the ``topology'' of a smooth projective variety and a (``general'') hyperplane section. Recent results of Nori produce cohomological evidence for a conjecture that…
Four-dimensional gravity admits many equivalent formulations - metric, Einstein-Cartan, teleparallel, McDowell-Mansouri, among others - each offering distinct advantages, particularly, in view of quantization. We propose a new formulation…
This reports on the fundamental objects revealed by Ross Street, which he called `orientals'. Street's work was in part inspired by Robert's attempts to use N-category ideas to construct nets of C*-algebras in Minkowski space for…
The early history of the universe might be described by a topological phase followed by a standard second phase of Einstein gravity. To study this scenario in its full generality, we consider a four-manifold of Euclidean signature in the…
We find the general solution to the twisting equation in the tensor bialgebra $T({\bf R})$ of an associative unital ring ${\bf R}$ viewed as that of fundamental representation for a universal enveloping Lie algebra and its quantum…
We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…
We construct a global geometric model for complex analytic equivariant elliptic cohomology for all compact Lie groups. Cocycles are specified by functions on the space of fields of the two-dimensional sigma model with background gauge…
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…
We construct an explicit canonical cycle in the top-dimensional homology of the Voronoi complex associated with an arithmetic group. This cycle relates to the cohomology of SL$_n(\mathbb{Z})$ with rational coefficients at the virtual…
Using equivariant obstruction theory we construct equivariant maps from certain classifying spaces to representation spheres for cyclic groups, product of elementary Abelian groups and dihedral groups. Restricting them to finite skeleta…
The building blocks of Hudson-Parthasarathy quantum stochastic calculus start with Weyl operators on a symmetric Fock space. To realize a relativistically covariant version of the calculus we construct representations of Poincare group in…
This paper investigates the interplay between the geometric and topological properties of spherically symmetric black hole metrics within Einstein gravity, emphasizing implications for Bose-Einstein Condensation (BEC). By analyzing metric…
We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show…
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain topological algebras. To this end we show that, for a continuous morphism $\phi: \X\to \Y$ of complexes of complete nuclear $DF$-spaces,…
This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using…
We define holomorphic structures on canonical line bundles of the quantum projective space $\qp^{\ell}_q$ and identify their space of holomorphic sections. This determines the quantum homogeneous coordinate ring of the quantum projective…
In this paper, we construct various simple vertex superalgebras which are extensions of affine vertex algebras, by using abelian cocycle twists of representation categories of quantum groups. This solves the Creutzig and Gaiotto conjectures…
We present a generalized Ernst-type framework for stationary, axisymmetric spacetimes in which a scalar field is coupled to the electrodynamic field, with a particular focus on the ModMax theory. Our approach relies on the Weyl…