Related papers: Field Theory and the Standard Model
This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value…
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
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…
I present a somewhat selective review of microlensing theory, covering five major areas: 1) the derivation of the basic formulae, 2) the relation between the observables and the fundamental physical parameters, 3) binaries, 4) astrometric…
Field Theory on Event Symmetric space-time is constructed using the gauge group of discrete open strings. Models with invariant actions can be viewed as natural extensions of Matrix Models. The objective is to find a fundamental…
This is a set of four lectures presented at the Theoretical Advanced Study Institute (TASI-09) in June 2009. The goal of the lectures is to introduce students to some of the basic ideas and tools required for theoretical analysis of…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field…
In this work a class of massive scalar field theories with self-interactions described by a general potential is studied. Under the sole condition that the potential admits the Fourier representation, it is shown that such theories may be…
This is a write-up of lectures on integrable sigma-models, which covers the following topics: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
In this set of four lectures I will discuss some aspects of the Standard Model (SM) as a quantum field theory and related phenomenological observations which have played a crucial role in establishing the $SU(2)_{L} \times U(1)_{Y}$ gauge…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with…
In these six lectures, we examine what can be learnt about the behavior of multi-layer neural networks from the analysis of linear models. We first recall the correspondence between neural networks and linear models via the so-called lazy…
We define a sigma model with doubled target space and calculate its background field equations. These coincide with generalised metric equation of motion of double field theory, thus the double field theory is the effective field theory for…
This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems…