Abstract
In order to make the book as self-contained as possible we briefly outline the connection between Lie groups and Lie algebras using the familiar concepts of matrices and linear algebra. The special orthogonal groups in 2 and 3 dimensions, SO(2) and SO(3), are used as familiar examples. It is also shown how the infinitesimal group transformations corresponding to one-parameter subgroups give rise to the generators of the associated Lie algebra. Also we discuss the special unitary group SU(2), which is important for spin in quantum mechanics, and show its connection with SO(3).
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© 1994 Springer-Verlag Berlin Heidelberg
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Adams, B.G. (1994). Lie Groups and Lie Algebras. In: Algebraic Approach to Simple Quantum Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57933-2_12
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DOI: https://doi.org/10.1007/978-3-642-57933-2_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57801-7
Online ISBN: 978-3-642-57933-2
eBook Packages: Springer Book Archive