相关论文: Lectures on Lattices and locally symmetric spaces

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

These lectures are an introduction to the physics of strongly correlated fermions and bosons. They are specially targeted for the experimental realizations that have been provided by cold atomic gases in optical lattices.

Whoever has to learn or to teach thermodynamics is confronted with conceptual difficulties which are specific to this field of physics ([1],[2]). It seems that they can be eliminated by inserting relativity in the thermodynamic theory. The…

The aim of this introductory lecture is to review the arguments, according to which the symmetry properties of the strong interaction reveal themselves at low energies. I first discuss the symmetries of QCD, then sketch the method used to…

These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.

These notes are a written version of a set of lectures given at TASI-02 on the topic of effective field theories. They are meant as an introduction to some of the latest techniques and applications in the field.

Following recent assumptions to unify quantum mechanics and general relativity, the structure of spacetime is suppose to be a consequence of the relations among some fundamental objects, and its concept can be formulated without the…

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue…

These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic…

A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.

This chapter provides a pedagogical introduction to lattice quantum field theory, with strong emphasis on lattice quantum chromodynamics. The chapter reviews key foundational concepts of lattice quantum chromodynamics, as well as a broad…

We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students…

The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the…

This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…

The special theory of relativity has fundamentally changed our views of space and time. The relativity of simultaneity in particular, and the theory of relativity as a whole, still presents significant difficulty for beginners in the…

This course consists of two lectures. In the first lecture I discuss why a non perturbative formulation of QCD is needed, and I show that lattice formulation copes with this need, even if it mainly produces numerical results. In the second…

Wilson's formulation of lattice QCD is attractive for many reasons, but perhaps mainly because of its simplicity and conceptual clarity. Numerical simulations of the Wilson theory (and of its improved versions) tend to be extremely…