Related papers: From Conformal Haag-Kastler Nets to Wightman Funct…
Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also…
We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.
We suggest a method to compute the correlation functions in conformal quantum mechanics (CFT$_1$) for the fields that transform under a non-local representation of $\mathfrak{sl}(2)$ basing on the invariance properties. Explicit…
Conformal nets are a classical topic in quantum field theory: they assign operator algebras to one-dimensional manifolds, and have close connections with one-dimensional topological field theories. It seems to be well-known that the usual…
The goal of this article is to generalise the Witten deformation to even dimensional conic manifolds and a class of functions called admissible Morse functions.
We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D_{2n}-E_{6,8} Dynkin diagrams such…
The authors recently introduced so-called Vandermonde nets. These digital nets share properties with the well-known polynomial lattices. For example, both can be constructed via component-by-component search algorithms. A striking…
We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebras and conformal nets, we also obtain a complete…
A general two-dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Applying the generators of the closed subalgebra generated by…
In this thesis we study the momentum space approach to the solution of the CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the essential steps needed to build tensor correlators starting from the scalar solutions, for…
A recently proposed ab initio Hartree-Fock approach aimed at directly obtaining the Wannier functions of a crystalline insulator is applied to polymers. The systems considered are the LiH chain and trans-polyacetylene. In addition to being…
We exploit an ansatz in order to construct power series expansions for pairs of conjugate functions defined on domains of Euclidean $3$--space. Convergence properties of the resulting series are investigated. Entire solutions which are not…
We propose a method to holographically compute the conformal partial waves in any decomposition of correlation functions of primary operators in conformal field theories using open Wilson network operators in the holographic gravitational…
We produce two-dimensional contiguous relations for generalized hypergeometric functions by starting with linearization coefficients for some continuous generalized hypergeometric orthogonal polynomials in the Askey-scheme.
In this article a procedure to construct bent functions from $\F_{p^n}$ to $\F_p$ by merging plateaued functions which are bent on ($n-2$)-dimensional subspaces of $\F_{p^n}$ is presented. Taking advantage of such classes of plateaued…
Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a…
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on…
We study the low-energy limit of Wilson lines (charged impurities) in conformal gauge theories in 2+1 and 3+1 dimensions. As a function of the representation of the Wilson line, certain defect operators can become marginal, leading to…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…