LEADER 05356nam 2200673Ia 450 001 9910827536303321 005 20240418061956.0 010 $a1-281-46682-4 010 $a9786611466824 010 $a0-08-053266-7 035 $a(CKB)1000000000384202 035 $a(EBL)349344 035 $a(OCoLC)476165673 035 $a(SSID)ssj0000297972 035 $a(PQKBManifestationID)11261219 035 $a(PQKBTitleCode)TC0000297972 035 $a(PQKBWorkID)10343799 035 $a(PQKB)10318649 035 $a(MiAaPQ)EBC349344 035 $a(Au-PeEL)EBL349344 035 $a(CaPaEBR)ebr10235983 035 $a(CaONFJC)MIL146682 035 $a(PPN)17892850X 035 $a(EXLCZ)991000000000384202 100 $a19830708d1997 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGroup theory in physics$b[electronic resource] $ean introduction /$fJ.F. Cornwell 205 $a1st ed. 210 $aSan Diego $cAcademic Press$dc1997 215 $a1 online resource (361 p.) 225 1 $aTechniques of physics ;$v7 300 $aDescription based upon print version of record. 311 $a0-12-189800-8 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Group Theory in Physics: An Introduction; Copyright Page; Contents; Preface; Chapter 1. The Basic Framework; 1. The concept of a group; 2. Groups of coordinate transformations; 3. The group of the Schro?dinger equation; 4. The role of matrix representations; Chapter 2. The Structure of Groups; 1. Some elementary considerations; 2. Classes; 3. Invariant subgroups; 4. Cosets; 5. Factor groups; 6. Homomorphic and isomorphic mappings; 7. Direct products and semi-direct products of groups; Chapter 3. Lie Groups; 1. Definition of a linear Lie group 327 $a2. The connected components of a linear Lie group3. The concept of compactness for linear Lie; 4. Invariant integration; Chapter 4. Representations of Groups - Principal Ideas; 1. Definitions; 2. Equivalent representations; 3. Unitary representations; 4. Reducible and irreducible representations; 5. Schur's Lemmas and the orthogonality theorem for matrix representations; 6. Characters; Chapter 5. Representations of Groups - Developments; 1. Projection operators; 2. Direct product representations; 3. The Wigner-Eckart Theorem for groups of coordinate transfor-mations in IR3 327 $a4. The Wigner-Eckart Theorem generalized5. Representations of direct product groups; 6. Irreducible representations of finite Abelian groups; 7. Induced representations; Chapter 6. Group Theory in Quantum Mechanical Calculations; 1. The solution of the Schro?dinger equation; 2. Transition probabilities and selection rules; 3. Time-independent perturbation theory; Chapter 7. Crystallographic Space Groups; 1. The Bravais lattices; 2. The cyclic boundary conditions; 3. Irreducible representations of the group T of pure primitive translations and Bloch's Theorem; 4. Brillouin zones 327 $a5. Electronic energy bands6. Survey of the crystallographic space groups; 7. Irreducible representations of symmorphic space groups; 8. Consequences of the fundamental theorems; Chapter 8. The Role of Lie Algebras; 1. ""Local"" and ""global"" aspects of Lie groups; 2. The matrix exponential function; 3. One-parameter subgroups; 4. Lie algebras; 5. The real Lie algebras that correspond to general linear Lie groups; Chapter 9. The Relationships between Lie Groups and Lie Algebras Explored; 1. Introduction; 2. Subalgebras of Lie algebras; 3. Homomorphic and isomorphic mappings of Lie algebras 327 $a4. Representations of Lie algebras5. The adjoint representations of Lie algebras and linear Lie groups; 6. Direct sum of Lie algebras; Chapter 10. The Three-dimensional Rotation Groups; 1. Some properties reviewed; 2. The class structures of SU(2) and SO(3); 3. Irreducible representations of the Lie algebras su(2) and so(3); 4. Representations of the Lie groups SU(2), SO(3) and O(3); 5. Direct products of irreducible representations and the Clebsch-Gordan coefficients; 6. Applications to atomic physics; Chapter 11. The Structure of Semi-simple Lie Algebras; 1. An outline of the presentation 327 $a2. The Killing form and Cartan's criterion 330 $aThis book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and apprec 410 0$aTechniques of physics ;$v7. 606 $aGroup theory 606 $aMathematical physics 615 0$aGroup theory. 615 0$aMathematical physics. 676 $a530.1522 700 $aCornwell$b J. F$045925 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827536303321 996 $aGroup theory in physics$9167868 997 $aUNINA