Author | Pfeifer, Walter. author |
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Title | The Lie Algebras su(N) [electronic resource] : An Introduction / by Walter Pfeifer |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8097-8 |
Descript | X, 432 p. online resource |
1 Lie algebras -- 1.1 Definition and basic properties -- 1.2 Isomorphic Lie algebras -- 1.3 Operators and functions -- 1.4 Representation of a Lie algebra -- 1.5 Reducible and irreducible representations -- 2 The Lie algebras su(N) -- 2.1 Hermitian matrices -- 2.2 Definition -- 2.3 Structure constants of su(N) -- 3 The Lie algebra su(2) -- 3.1 The generators of the su(2)-algebra -- 3.2 Operators constituting the algebra su(2) -- 3.3 Multiplets of su(2) -- 3.4 Irreducible representations of su(2) -- 3.5 Direct products of irreducible representations -- 3.6 Reduction of direct products of su(2) -- 3.7 Graphical reduction of direct products -- 4 The Lie algebra su(3) -- 4.1 The generators of the su(3)-algebra -- 4.2 Subalgebras of the su(3)-algebra -- 4.3 Step operators and states in su(3) -- 4.4 Multiplets of su(3) -- 4.5 Individual states of the su(3)-multiplet -- 4.6 Dimension of the su(3)-multiplet -- 4.7 The smallest su(3)-multiplets -- 4.8 The fundamental multiplet of su(3) -- 4.9 The hypercharge Y -- 4.10 Irreducible representations of the su(3) algebra -- 4.11 Casimir operators -- 4.12 The eigenvalue of the Casimir operator C1 in su(3) -- 4.13 Direct products of su(3)-multiplets -- 4.14 Decomposition of direct products of multiplets -- 5 The Lie algebra su(4) -- 5.1 The generators of the su(4)-algebra, subalgebras -- 5.2 Step operators and states in su(4) -- 5.3 Multiplets of su(4) -- 5.4 The charm C -- 5.5 Direct products of su(4)-multiplets -- 5.6 The CartanโWeyl basis of su(4) -- 6 General properties of the su(N)-algebras -- 6.1 Elements of the su(N)-algebra -- 6.2 Multiplets of su(N) -- References