03710nam a2200313 a 4500 00006226 WSP 20230529172017.0 m d cr buu|||uu||| 091123s2014 si a sb 001 0 eng d 9789814603287 WSPC eng WSPC 512.55 Das, Ashok and Okubo, Susumu Lie Groups and Lie Algebras for Physicists Singapore ; World Scientific Pub. Co., ©2014. 360 p. : Includes bibliographical references and index. 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. 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. 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. Electronic books. 9789814603270 http://www.worldscientific.com/worldscibooks/10.1142/9169#t=toc ebook ddc EBK 2368 2368 0 0 ddc 0 0 IITTP IITTP 2018-02-06 0 512.55 EB00298 2018-02-06 00:00:00 2018-02-06 EBK