Gauge Theories and the Standard Model

Guido Altarelli,Stefano Forte

doi:10.1007/978-3-030-38207-0_2

Abstract

AbstractThis chapter, Chaps.10.1007/978-3-030-38207-0_3and10.1007/978-3-030-38207-0_4present a self-contained introduction to the Standard Model of fundamental interactions, which describes in the unified framework of gauge quantum field theories all of the fundamental forces of nature but gravity: the strong, weak, and electromagnetic interactions. This set of chapters thus provides both an introduction to the Standard Model, and to quantum field theory at an intermediate level. The union of the three chapters can be taken as a masters’ level course reference, and it requires as a prerequisite an elementary knowledge of quantum field theory, at the level of many introductory textbooks, such as Vol. 1 of Aitchison-Hey, or, at a somewhat more advanced level, Maggiore. The treatment is subdivided into three parts, each corresponding to an individual chapter, with more advanced field theory topics introduced along the way as needed. Specifically, this chapter presents the general structure of the Standard Model, its field content, and symmetry structure. This involves an introduction to non-abelian gauge theories both at the classical and quantum level. Also, it involves a discussion of spontaneous symmetry breaking and the Higgs mechanism, that play a crucial role in the architecture of the Standard Model, and their interplay with the quantization of gauge theories. Chapter10.1007/978-3-030-38207-0_3then presents the electroweak sector of the Standard Model. This requires introducing the concepts of CP violation and mixing, and of radiative corrections. Finally, Chap.10.1007/978-3-030-38207-0_4presents the strong sector of the theory, which requires a more detailed treatment of renormalization and the renormalization group.

Highlights

The dozen or so years since the original writing of these chapter have seen a full vindication of the Standard Model as a correct and accurate theory, and have stimulated a vast number of highly sophisticated experimental and theoretical results which build upon the treatment presented below
The ultimate goal of fundamental physics is to reduce all natural phenomena to a set of basic laws and theories that, at least in principle, can quantitatively reproduce and predict the experimental observations
In atoms the electrons are bound to nuclei by electromagnetic forces and the properties of electron clouds explain the complex phenomenology of atoms and molecules

Summary

Chapter 2

The presentation of the Standard Model, Chaps. 3 and 4 was originally written by Guido Altarelli in 2007 In this introduction we provide a brief update (with references), and a discussion of the main developments which have taken place since the time of the writing. The only aspects of the presentation which require (minimal) updating are the numerical values given for parameters, such as the Fermi coupling constant GF , see Eq (2.3). All of these parameters have been known quite accurately since the early 2000s

Altarelli University of Rome 3, Rome, Italy

Introduction

Overview of the Standard Model

The Formalism of Gauge Theories

Application to QCD

Quantization of a Gauge Theory

Spontaneous Symmetry Breaking in Gauge Theories

Quantization of Spontaneously Broken Gauge Theories