Greiner W., Mueller B. — Quantum mechanics: symmetries :: Электронная библиотека попечительского совета мехмата МГУ

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Greiner W., Mueller B. — Quantum mechanics: symmetries

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Название: Quantum mechanics: symmetries

Авторы: 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.

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Рубрика: Физика/Общие курсы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1994

Количество страниц: 496

Добавлена в каталог: 09.09.2005

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Предметный указатель

$J/\Psi$ meson      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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