Related papers: The Capitulation Problem in Class Field Theory
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
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 first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over ${\mathbb Q}$. More generally, we show that over such a field, every split differential…
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
The exact solution of the Cauchy problem of the linear theory of elasticity is given in the paper, when the initial data belong to a specific class of functions.
This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…
We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
We consider a two-dimensional conformal field theory which contains two kinds of the bosonic degrees of freedom. Two linear dilaton fields enable us to study a more general case. Various properties of the model such as OPEs, central charge,…
We use higher ideles and duality theorems to develop a universal approach to higher dimensional class field theory.
This paper establishes an equivalence between the halting problem in computability theory and the convergence of power series in mathematical analysis.
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number…
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
In this work we introduce new scalar field models and study the defect solutions they may engender. The investigation is based on the deformation procedure, which greatly simplify the calculations, leading us to new models together with the…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
We investigate a class of nonlinear nonautonomous scalar field equations with fractional diffusion, critical power nonlinearity and a subcritical term. The involved potentials are allowed for vanishing behavior at infinity. The problem is…
We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie…