Related papers: Potential theory and applications in conformal geo…

A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction…

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…

The development of cubical type theory inspired the idea of "extension types" which has been found to have applications in other type theories that are unrelated to homotopy type theory or cubical type theory. This article describes these…

We discuss a class of regions and conformal mappings which are useful in several problems of approximation theory, harmonic analysis and spectral theory.

Parametric geometry of numbers is a new theory, recently created by Schmidt and Summerer, which unifies and simplifies many aspects of classical Diophantine approximations, providing a handle on problems which previously seemed out of…

We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…

In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions…

This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis…

The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…

Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…

We discuss qualitative features of the conformal relation between certain classes of gravity theories and general relativity, common to different themes such as $f(R)$, Brans-Dicke-type, and string theories. We focus primarily on the frame…

Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…

The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian…

A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…

We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…

We extend results of parametric geometry of numbers to a general diagonal flow on the space of lattices. Moreover, we compute the Hausdorff dimension of the set of trajectories with every given behavior, with respect to a nonstandard metric…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

The postulate of universal Weyl conformal symmetry for all elementary physical fields introduces nonclassical gravitational effects in both conformal gravitation(CG) and the conformal Higgs model (CHM). The resulting theory is found to…