Mathematical gauge theory. With applications to the standard model of particle physics
type: Item
instance of: scholarly article
title: Mathematical gauge theory. With applications to the standard model of particle physics
zbMATH Open document ID: 1390.81005
DOI: 10.1007/978-3-319-68439-0
author: M. J. D. Hamilton
published in: Universitext
publication date: 2017-10-26T00:00:00Z
review text: Assuming an introductory course on differential geometry and some basic knowledge of special relativity, both of which are summarized in the appendices, the book expounds the mathematical background behind the well-established standard model of modern particle and high energy physics. The book is based upon the author's lecture notes for graduate courses at the university of Stuttgart and the LMU Munich in Germany. The first six chapters of the book discuss mathematical foundations, while the remaining three chapters are concerned with the standard model of elementary particle physics. I believe that the book will be a standard textbook on the standard model for mathematics-oriented students. The standard model of elementary particles is a gauge theory with Lie group \[ \mathbf{SU}(3) \times\mathbf{SU}(2) \times \mathbf{U}(1) \] while grand unified theories are based on such Lie groups as \[ \mathbf{SU}(5). \] The first chapter gives basic concepts about Lie groups and Lie algebras, including correspondences between Lie groups and Lie algebras as well as Cartan's theorem on closed subgroups on the lines of [\textit{H. Baum}, Eichfeldtheorie. Eine Einführung in die Differentialgeometrie auf Faserbündeln. 2nd revised ed. Heidelberg: Springer Spektrum (2014; Zbl 1297.53001); Eichfeldtheorie. Eine Einführung in die Differentialgeometrie auf Faserbündeln. Berlin: Springer (2009; Zbl 1175.53001); \textit{T. Bröcker} and \textit{T. tom Dieck}, Representations of compact Lie groups. Corrected reprint of the 1985 orig. New York, NY: Springer (1995; Zbl 0874.22001); Representations of compact Lie groups. New York: Springer (1985; Zbl 0581.22009)]. Three Dirac spinors for each quark flavor gather together to form a vector in a representation space \(\mathbb{C}^{3}\) of the gauge group \(\mathbf{SU}(3)\) of quantum chromodynamics, while two left-handed Weyl spinors gather together to form a vector in a representation space \(\mathbb{C}^{2}\) of the gauge group \(\mathbf{SU}(2) …
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81V22
Mathematics Subject Classification ID: 55Q91
Mathematics Subject Classification ID: 81R25
Mathematics Subject Classification ID: 81T18
Mathematics Subject Classification ID: 70S05
Mathematics Subject Classification ID: 81R40
zbMATH DE Number: 6798759
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-68439-0
OpenAlex ID: W4242038705
description: scientific article; zbMATH DE number 6798759