相关论文: Lectures on Lattices and locally symmetric spaces

It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points…

These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…

In this notes we show how a problem regarding continued fractions of rational numbers, lead to several phenomena in number theory and dynamics, and eventually to the problem of shearing of divergent diagonal orbits in the space of adelic…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…

The purpose of these lecture notes is to describe the gravitational lens effects in different astrophysical contexts. These notes are voluntarily focused on the fundamental mechanisms and the basic concepts that are useful to describe these…

Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by non-principal ideals yields simple…

These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…

In this talk I want to convey an idea about the perspectives for precise lattice QCD computations. Some emphasis is put on the field of flavour physics, where lattice QCD seems to be needed the most in the quantitative interpretation of…

These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.

We introduce a framework of structural approximation to represent Lorentz-invariant Minkowski space-time as the limit of finite cyclic lattices, each equipped with the action of a finite quasi-Lorentz group. This construction provides a…

This paper gives a short introduction into the metric theory of spaces with dilations.

In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…

This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence, a precise dictionary that describes the emergence of continuum quantum theories from finite, nonperturbatively defined models…

This is the written version of four lectures given at the 1994 TASI. My aim is to explain the essentials of lattice calculations, give an update on (though not a review of) the present status of calculations of phenomenologically…

This letter is in response to a recent review by DeTar and Gottlieb about lattice QCD that has recently appeared in Physics Today. It also is partially motivated by a separate review written by DeGrand. My basic point is that one should be…

I give a review of existing frameworks, which are designed to analyse lattice data in the three-particle sector. A particular emphasis is laid on the foundations of the theory, where the separation of the short- and long-range effects plays…

String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string…

The aim of this lecture is to discuss in some detail two simple but important problems which have considerable importance for the development of theoretical work in semiclassical dense matter physics.

In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…