Das, Ashok and Okubo, Susumu creator text bibliography Electronic books. si Singapore World Scientific Pub. Co. ©2014 2014 monographic eng

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360 p. : The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras. 1. Introduction to groups. 1.1. Definition of a group. 1.2. Examples of commonly used groups in physics. 1.3. Group manifold. 1.4. References -- 2. Representation of groups. 2.1. Matrix representation of a group. 2.2. Unitary and irreducible representations. 2.3. Group integration. 2.4. Peter-Weyl theorem. 2.5. Orthogonality relations. 2.6. Character of a representation. 2.7. References -- 3. Lie algebras. 3.1. Definition of a Lie algebra. 3.2. Examples of commonly used Lie algebras in physics. 3.3. Structure constants and the Killing form. 3.4. Simple and semi-simple Lie algebras. 3.5. Universal enveloping Lie algebra. 3.6. References -- 4. Relationship between Lie algebras and Lie groups. 4.1. Infinitesimal group and the Lie algebra. 4.2. Lie groups from Lie algebras. 4.3. Baker-Campbell-Hausdorff formula. 4.4. Ray representation. 4.5. References -- 5. Irreducible tensor representations and Young tableau. 5.1. Irreducible tensor representations of U(N). 5.2. Young tableau. 5.3. Irreducible tensor representations of SU(N). 5.4. Product representation and branching rule. 5.5. Representations of SO(N) groups. 5.6. Double valued representation of SO(3). 5.7. References -- 6. Clifford algebra. 6.1. Clifford algebra. 6.2. Charge conjugation. 6.3. Clifford algebra and the O(N) group. 6.4. References -- 7. Lorentz group and the Dirac equation. 7.1. Lorentz group. 7.2. Generalized Clifford algebra. 7.3. Dirac equation. 7.4. References -- 8. Yang-Mills gauge theory. 8.1. Gauge field dynamics. 8.2. Fermion dynamics. 8.3. Quantum chromodynamics. 8.4. References -- 9. Quark model and SU[symbol](3) symmetry. 9.1. SU[symbol] flavor symmetry. 9.2. SU[symbol](3) flavor symmetry breaking. 9.3. Some applications in nuclear physics. 9.4. References -- 10. Casimir invariants and adjoint operators. 10.1. Computation of the Casimir invariant I(p). 10.2. Symmetric Casimir invariants. 10.3. Casimir invariants of so(N). 10.4. Generalized Dynkin indices. 10.5. References -- 11. Root system of Lie algebras. 11.1. Cartan-Dynkin theory. 11.2. Lie algebra A[symbol] = su([symbol]+ 1). 11.3. Lie algebra D[symbol] = so(2[symbol]). 11.3.1. D4 = so(8) and the triality relation. 11.4. Lie algebra B[symbol] = so(2[symbol] + 1). 11.5. Lie algebra C[symbol] = sp(2[symbol]). 11.6. Exceptional Lie algebras. 11.7. References. Includes bibliographical references and index. Electronic reproduction. Singapore : World Scientific Publishing Co., 2014. System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions. Lie algebras Group theory 512.55 9789814603287 http://www.worldscientific.com/worldscibooks/10.1142/9169#t=toc http://www.worldscientific.com/worldscibooks/10.1142/9169#t=toc WSPC 091123 20230529172017.0 00006226 eng