Symmetries and group theory in particle physics. An introduction to space-time and internal symmetries.
type: Item
instance of: scholarly article
title: Symmetries and group theory in particle physics. An introduction to space-time and internal symmetries.
zbMATH Open document ID: 1243.81005
DOI: 10.1007/978-3-642-15482-9
author: Giovanni Costa
author: G. L. Fogli
published in: Lecture Notes in Physics
publication date: 2010-10-15T00:00:00Z
review text: The aim of the monograph is two-fold, to give the basic notions and facts from group and group representation theory for particle physics and to give a survey of their applications in relativistic quantum field theory and particle physics. Therefore it should be considered to be a good handbook. Chapter 1 introduces the basic notions of Lie groups and algebras including the semi-simple Lie algebras and their representations together with Dynkin diagrams and classification of the classical semi-simple Lie algebras and Lie groups. Chapter 2 gives a short account of the main properties of the three-dimensional rotation group \(\mathrm{SO}(3)\) and its universal covering group \(\mathrm{SU}(2)\) as illustration of the contents of Chapter 1. It contains also the irreducible representations of \(\mathrm{SO}(3)\) and \(\mathrm{SU}(2)\) and introduces the Clebsch-Gordan coefficients. In Chapter 3 general properties of the homogeneous Lorentz transformations are considered paying basic attention to their group-theoretical aspects, which are important for special relativity in the description of elementary particle physics. The restricted Lorentz group \(L_{+}^{\uparrow}\) is analyzed through derivation of Lie algebra from its infinitesimal transformations. Irreducible representations of the group \(L_{+}^{\uparrow}\) and of the complete Lorentz group are discussed. In Chapter 4 the general properties of the Poincaré group (i.e. the group of inhomogeneous Lorentz transformations) are given as the space-time coordinate transformations between any two inertial frames of reference. Then, unitary irreducible representations of this group are considered, which are needed for the description of the quantum-mechanical states of one or more particles in Chapter 5. Chapter 6 analyzes the properties of the discrete operations, space inversion \(I_{s}\) and time reversal \(I_{t}\), belonging to the complete Lorentz group \(L\) and the Poincaré group \(P\). The transformation properties …
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81V25
zbMATH DE Number: 5800327
zbMATH Keywords: group representations theory
zbMATH Keywords: applications to particle physics
zbMATH Keywords: relativistic quantum field theory
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-15482-9
OpenAlex ID: W4250932149
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description: scientific article; zbMATH DE number 5800327