 Basic Representation TheoryNadir Jeevanjee ()
Chapter Chapter 5 in An Introduction to Tensors and Group Theory for Physicists, 2011, pp 145-212 from Springer Abstract: Abstract Chapter 5 discusses representation theory, which formalizes the notion of an object that transforms in a certain way under a given transformation (e.g. vectors under rotations, or antisymmetric tensors under boosts). We begin by defining a representation of a group as a vector space on which that group acts, and we give many examples, using the vector spaces we met in Chap. 2 and the groups we met in Chap. 4 . We then discuss how to take tensor products of representations, and we see how this reproduces the additivity of quantum numbers in Quantum Mechanics. We then define irreducible representations, which are in a sense the ‘smallest’ ones we can work with, and we compute these representations for SU(2). These just end up being the familiar spin j representations, where j is a half-integer. We then use these results to compute the irreducible representations of the Lorentz group as well. Keywords: Tensor Product; Irreducible Representation; Invariant Subspace; Double Cover; Equivalent Representation (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4715-5_5 Ordering information: This item can be ordered from DOI: 10.1007/978-0-8176-4715-5_5 Access Statistics for this chapter More chapters in Springer Books from Springer |
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