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Greiner W., Mueller B. — Quantum mechanics: symmetries
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Название: Quantum mechanics: symmetriesАвторы: Greiner W., Mueller B. Аннотация: Quantum Mechanics (Symmetries) deals with a particularly appealing and successful concept in advanced quantum mechanics. After a brief introduction to symmetries in classical mechanics, the text turns to their relevance in quantum mechanics, the consequences of rotation symmetry, and the general theory of Lie groups. The isospin group, hypercharge, SU(3) and their applications are all dealt with in depth before chapters on charm, SU(4), and dynamical symmetries lead to the frontiers of research in particle physics. This unique text comprises more than 120 detailed, worked examples and problems.As the third reprint of the second edition, this book has been revised to bring the text up to date.
Язык: Рубрика: Физика /Общие курсы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: second editionГод издания: 1994Количество страниц: 496Добавлена в каталог: 09.09.2005Операции: Положить на полку |
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365 398 Abelian transformation group 92 action 9 Active execution of symmetry operation 18 Active rotation 36 Adjoint representation 149 Airy function 399 Airy function, differential equation for 402 Angular momentum algebra 53 Angular momentum operator 30 Angular momentum operators in matrix representation 45 Antibaryons 179 Antiquarks 231 Antisymmetric state 293 Antisymmetrization operator 293 Antisymmetry relation 84 Antitriplet 224 Antiunitarity operators 445 asymptotic freedom 385 Axial vector 444 Axial vector, mesons 240 Baryon 176 231 Baryon decuplet, wave function of 264 Baryon multiplets 387 Baryon nonet 177 Baryon number 378 Baryon octet 207 Baryon octet, spin-flavour wave function of 267 Baryon properties of 177 Baryon resonance 179 217 Baryon resonances, hypercharge of 179 Baryon resonances, isospin of 231 Basis functions 293 Basis tensors 300 Beauty quark 410 412 Beta decay 235 Bottom quark 410 412 Broken symmetry, weakly 104 Cabbibo-suppressed decay 389 Canonical momentum 4 ff. Cartan matrix 432 Cartan subalgebra 420 Cartan — Weyl basis 420 Cartan — Weyl normalization 424 Cartesian representation 65 Cartesian representation of vector field 63 Casimir operator 327 Casimir operator of a fundamental representation of SU(n) 375 Casimir operator of abelian Lie groups 109 Casimir operator of SO(2,1) 480 Casimir operator of SU(2) 186 Casimir operator of SU(3) 191 197 Casimir operator of the isospin group 161 Casimir operator of the rotation group 106 Casimir operator, completeness of 109 Casimir, Hendrik 126 Centre-of-mass system 2 Charge multiplet 175 Charge operator 217 Charm 365 Charm, quantum numbers 367 Charm, quark 243 367 Charmonium 383 398 Charmonium, model 383 Charmonium, potential model of 398 Chiral group 241 Classical angular momentum 4 Classical Lie algebras, representation of 436 Clebsch — Gordon coefficients 67 ff. Clebsch — Gordon coefficients for spin-orbit coupling 76 Clebsch — Gordon coefficients of isospin 216 Clebsch — Gordon coefficients of SU(3) 254 Clebsch — Gordon coefficients, calculation of 71 ff. Clebsch — Gordon coefficients, evaluation of 70 Clebsch — Gordon coefficients, recursion relations 72 Clebsch — Gordon matrix 73 Clebsch, Rudolf Friedrich Alfred 79 Closed algebra 83 Coleman — Glashow relation 251 Colour 289 Commutation relations 28 Commutator 23 Compact Lie algebra 101 Compact Lie group 37 183 Compound nucleus 169 Condon — Shortley phase 57 Congredient transformation 37 Conjugate diagram 307 Conjugate Young diagram 306 Conservation law 15 Conservation law in homogeneous electromagnetic fields 15 Conservation law of angular momentum 5 Conservation of momentum 13 Conservation of total angular momentum 44 Conservation of total energy 3 Conservative systems 3 Conserved quantities 8 ff. Constant of motion 21 Continuous group 81 Continuous invariant subgroup 94 Continuous transformation 10 Contragredient transformation 36 Coordinate space 19 Coordinate transformation 8 ff. Coupling of the fundamental multiplet 228 Cross-section 170 Decuplet representation of SU(3) 313 Degeneracy of states 22 Degenerate states 104 Deuteron 140 ff. 164 Diagram, self-conjugate 317 Differential operator 43 Dimension of the representation D(p,q) 214 Displacement operator 34 Doublet 101 Doubly continuously connected group 38 Down quark 219 Dynamic symmetries 9 Dynamical symmetry of geometrical variable 456 Dynkin diagrams 428 ff. Dynkin diagrams, table of 431 Eckart, Carl Henry 174 Eigenfunctions 53 ff. Eigenfunctions of the total angular momentum operator 66 Eigenvalues of angular momentum operator 58 Eigenvector 22 Einstein's sum convention 35 Elementary representations of SU(3) 226 Energy conservation 3 Energy degeneracy of rotation group 131 Energy operator 31 Equations of motion 8 ff. Equations of motion for states shifted in space 20 Equivalence classes 331 ff. Essential degeneracy 306 Eta resonance 242 Euclidean group E(3) 121 Euler — Lagrange equations 1 ff. Exotic meson states 288 Exotic quark states 285 F-operator, spherical representation of 190 F-spin 190 F-spin algebra 198 Fine structure 78 Finite group element, of rotation group 82 Finite rotations 39 ff. Flavour hypercharge 390 Flavour isospin 390 G-Parity 154 ff. Galilean invariance 11 Galilei transformations 12 Gell-Mann — Nishijima relation 177 379 Gell-Mann — Nishijima relation, generalization of 388 Gell-Mann — Okubo mass formula 252 Gell-Mann, Murray 181 Generator 27 Generator for translational symmetry 26 Generator of a group 81 Generator of rotations 41 Generator of rotations for vector fields 45 Generator of SO(3) 53 Generator of SU(3) 187 220 Generator of the group 20 Generator of the Lie group SO(3) 51 Geometric symmetries 8 Global homogeneity of space 12 Group 33 Group Abelian 33 group characters 336 Group characters, definition of 327 Group continuous 33 group element 39 Group elements, conjugate 331 Group generators, normalization of 149 Group homomorphism 124 Group integration 339 Group isomorphism 124 Group multiplication 33 Group of Lorentz transformations 33 Group of rotations 33 Group of spatial displacements 35 Group of the residue classes 325 Group of translations 34 Group parameter 39 Group representation, invariant properties of 327 Group SO(3) 333 Group SU(n) 183 Group theory 33 Group U(N) 183 Guersey — Radicati mass formula 283 Hamiltonian 21 ff. Heisenberg algebra 97 Hermitian vector operator 46 Hidden charm 382 398 Hilbert space 19 Homogeneity of space 1 f. Homogeneity of time 2 Homomorphism of groups 124 Hypercharge 176 ff. 378 Hyperons 217 Ideal 93 ff. Ideal, abelian 94 Infinitesimal element, of rotation group 82 Infinitesimal rotation 3 Infinitesimal transformation 9 f. Integral of motion 10 Internal angular momentum 4 Intrinsic angular momentum 45 Intrinsic energy 354 Invariance 1 Invariance of the laws of nature 35 Invariance under a symmetry group 104 Invariant operator 101 Invariant operator, construction of 108 Invariant subgroups 93 Invariant subgroups, abelian 93 Invariant subspace 57 Invariant subspace of the rotation group 94 Invariant subspace, reduction of 94 Inverse element 33 Inversion group 113 Irreducibility, criterion for 337 Irreducible invariant subspace 94 Irreducible representation 59 Irreducible representation of permutation group 307 Irreducible representation of SU(2) 308 Irreducible representation of SU(n) 310 Irreducible representation of the rotation group 57 Iso-invariance 142 Iso-rotation operator 136 Iso-spinor 136 Iso-vector operator 153 ff. Isobaric charge multiplet 139 Isobaric group 113 Isobaric spin 139 Isobars 139 Isolated systems 2 Isomorphism of groups 124 Isomorphism of the rotation group 38 Isospin 217 Isospin doublet 218 Isospin group 159 Isospin group SU(2) 218 Isospin invariance, experimental test of 159 Isospin multiplet 167 Isospin operator for a multinucleon system 139 Isospin singlet 141 Isospin space 153 Isospin transformation 152 Isospin triplet 141 Isospin vector 153 Isospin vectors, transformation law for 153 Isotropic oscillator, classical 458 Isotropic oscillator, quantum mechanical 458 Isotropy of space 3 J particle 398 J-resonance 243 Jacobi identity 83 K-mesons 233 ff. Kaon resonance 242 Kepler problem, classical 453 Ket 18 Killing form 98 kinetic energy 11 Kronecker product 34 Lagrange equations 3 Lagrange function 2 ff. Lagrangian 15 Lie algebra 413 Lie algebra of groups with continuous invariant subgroups 94 Lie algebra of rank 1 425 Lie algebra of rank 2 426 Lie algebra of rank l>2 426 Lie algebra of SO(3) 118 Lie algebra of SO(n) 118 Lie algebra of spin-1, matrix representation of 117 Lie algebra of SU(2) 187 Lie algebra of SU(3) 190 ff. Lie algebra, classical 413 427 Lie algebra, exceptional 427 Lie algebra, regular representation of 146 Lie algebra, representation of 146 Lie algebra, semi-simple 413 Lie group 37 ff. Lie group, compact 473 483 Lie group, fundamental properties of 81 Lie group, non-compact 473 483 Lie's theorem 92 Lie, Sophus 51 Local homogeneity of space 13 Local measurements 16 Lorentz force 16 Lorentz group 37 Lorentz group, infinitesimal transformations of 88 Lorentz group, non-compactness 476 Lorentz transformation 19 Lorentz transformation, generators of 88 Lorentz transformation, structure constants of 88 Lorentz — Minkowski metric 88 Magnetic moment of quarks 284 ff.
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