The Lie Algebras su(N)
Subtitle: An Introduction
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: September 17, 2003
Language: eng
Format: Paperback
Number of pages: 116
ISBN-13: 9783764324186
Subjects: Algebra; Mathematics; Geometry - General; Science/Mathematics; Algebra - General; Mathematical Physics; Lie algebra; Lie algebras; Mathematics / Algebra / General; Mathematics-Geometry - General; Nonassociative rings; Representation theory; Science-Mathematical Physics; Algebra - Abstract; Group Theory
First sentence: A Lie algebra comprises the elememts a, b, c, . . . , which may be general matrices or matrices with certain properties (real/complex matrix elements, internal symmetries) or linear operators etc.
Description: Lie algebras are efficient tools for analyzing the properties of physical systems. Concrete applications comprise the formulation of symmetries of Hamiltonian systems, the description of atomic, molecular and nuclear spectra, the physics of elementary particles and many others. This work gives an introduction to the properties and the structure of the Lie algebras su(n). First, characteristic quantities such as structure constants, the Killing form and functions of Lie algebras are introduced. The properties of the algebras su(2), su(3) and su(4) are investigated in detail. Geometric models of the representations are developed. A lot of care is taken over the use of the term "multiplet of an algebra". The book features an elementary (matrix) access to su(N)-algebras, and gives a first insight into Lie algebras. Student readers should be enabled to begin studies on physical su(N)-applications, instructors will profit from the detailed calculations and examples.