Related papers: Field patching, factorization and local-global pri…

It has been recently observed that fundamental aspects of the classical theory of factorization can be greatly generalized by combining the languages of monoids and preorders. This has led to various theorems on the existence of certain…

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…

We give a self-contained proof of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa's book. In the revised version, (i) positive characteristic case is included, (ii) the proof of…

We give defining equations for function fields over finite fields with many rational places. They are obtained from composita of quadratic extensions of the rational function field.

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling operators at the two-dimensional percolation…

We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (infinity,d)-category of bordisms with geometric data, such as Riemannian metrics or geometric string structures, and…

In this paper, we obtain some factorization results on formal power series over principle ideal domains with sharp bounds on number of irreducible factors. These factorization results correspondingly lead to irreducibility criteria for…

A rigorous theoretical framework is developed for a generalized local frame transformation theory (GLFT). The GLFT is applicable to the following systems: to Rydberg atoms or molecules in an electric field, or to negative ions in any…

We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical…

Interpretability techniques aim to provide the rationale behind a model's decision, typically by explaining either an individual prediction (local explanation, e.g. 'why is this patient diagnosed with this condition') or a class of…

In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf…

We count the maximal lattices over $p$-adic fields and the rational number field. For this, we use the theory of Hecke series for a reductive group over nonarchimedean local fields, which was developed by Andrianov and Hina-Sugano. By…

We combine recent results of Clifton and Halvorson [1] with structural results of the author [2--5] concerning the local observables in thermofield theory. An number of interesting consequences are discussed.

Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…

We study an inverse acoustic scattering problem by the Factorization Method when the unknown scatterer consists of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each…

We construct compact descriptions of function fields and number fields.

In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are…

This article is based on recent works done in collaboration with M. Mintchev, E. Ragoucy and P. Sorba. It aims at presenting the latest developments in the subject of factorization for integrable field theories with a reflecting and…

We recall a natural framework to deal with local field theory in which bare amplitudes are completely finite. We first present the main general properties of this scheme, the so-called Taylor-Lagrange regularization scheme. We then…