Lie groups and lie algebras for physicists / Ashok Das, Susumu Okubo.

Format:

Book

Author/Creator:

Das, Ashok, author.

Okubo, Susumu, author.

Language:

English

Subjects (All):

Lie groups--Textbooks.

Lie groups.

Lie groups--Study and teaching (Higher).

Lie algebras.

Group theory.

Physical Description:

1 online resource (358 p.)

Place of Publication:

Singapore : World Scientific Publishing Company, 2014.

Language Note:

English

Summary:

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. Contents: Introduction to Groups; Representation of Groups; Lie Algebras; Relationship between Lie Algebras and Lie Groups; Irreducible Tensor Representations and Young Tableau; Clifford Algebra; Lorentz Group and the Dirac Equation; Yang-Mills Gauge Theory; Quark Model and SU

Contents:

Preface; Contents; 1 Introduction to groups; 1.1 Definition of a group; 1.2 Examples of commonly used groups in physics; 1.2.1 Symmetric group SN; 1.2.2 One dimensional translation group T1; 1.2.3 One dimensional unitary group U(1); 1.2.4 U(N) and SL(N) groups; 1.2.5 O(N) and SO(N) groups; 1.2.6 Symplectic group Sp(2N); 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; 2.4.1 Fully reducible representation; 2.4.2 Unitary representation

2.5 Orthogonality relations2.6 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; 3.2.1 Lie algebra of gl(N) and sl(N); 3.2.2 Lie algebra of so(N); 3.2.3 Lie algebras of u(N) and su(N); 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 representation4.5 References; 5 Irreducible tensor representations and Young tableau; 5.1 Irreducible tensor representations of U(N); 5.2 Young tableau; 5.3 Irreducible tensor representationns 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; 6.1.1 Dimension of the representation; 6.1.2 Reducible representation; 6.1.3 Irreducible representation and its uniqueness; 6.2 Charge conjugation; 6.3 Clifford algebra and the O(N) group; 6.4 References

7 Lorentz group and the Dirac equation7.1 Lorentz group; 7.1.1 Proper orthochronous Lorentz group; 7.1.2 Orthochronous Lorentz group; 7.1.3 Improper Lorentz group; 7.2 Generalized Clifford algebra; 7.3 Dirac equation; 7.3.1 Charge conjugation; 7.3.2 Weyl and Majorana particles; 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 SUF (3) symmetry; 9.1 SUF flavor symmetry; 9.2 SUF (3) flavor symmetry breaking; 9.3 Some applications in nuclear physics; 9.4 References

10 Casimir invariants and adjoint operators10.1 Computation of the Casimir invariant I( ) ; 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 = su( + 1); 11.3 Lie algebra D = so(2 ):; 11.3.1 D4 = so(8) and the triality relation; 11.4 Lie algebra B = so(2 + 1):; 11.5 Lie algebra C = sp(2 ); 11.6 Exceptional Lie algebras; 11.6.1 G2; 11.6.2 F4; 11.6.3 E6; 11.6.4 E7; 11.6.5 E8; 11.7 References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed October 16, 2014).

ISBN:

981-4603-28-7