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Lie Algebras In Particle Physics: from Isospin To Unified Theories [Pehme köide]

  • Formaat: Paperback / softback, 344 pages, kõrgus x laius x paksus: 227x152x20 mm, kaal: 466 g
  • Ilmumisaeg: 22-Oct-1999
  • Kirjastus: Westview Press Inc
  • ISBN-10: 0738202339
  • ISBN-13: 9780738202334
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Lie Algebras In Particle Physics: from Isospin To Unified TheoriesSuurem pilt
  • Formaat: Paperback / softback, 344 pages, kõrgus x laius x paksus: 227x152x20 mm, kaal: 466 g
  • Ilmumisaeg: 22-Oct-1999
  • Kirjastus: Westview Press Inc
  • ISBN-10: 0738202339
  • ISBN-13: 9780738202334
Teised raamatud teemal:
Teised raamatud sellest sooduspakkumisest: Taylor & Francis teadusraamatud International Student Editions hindadega
Püsilink: https://www.kriso.ee/db/9780738202334.html
Märksõnad:
Georgi's Harvard lectures (he's taught physics there since 1980) discuss application of the theory of Lie Algebras and their representations to a wide variety of problems in particles physics and quantum mechanics. This edition has been expanded to include more extensive discussion of finite group theory and representations of the permutation group, as well as discussion of new subjects such as Dynkin indices, spontaneous symmetry breaking, lepton number as a fourth color, and the 27-dimensional representation of E(6). Annotation c. Book News, Inc., Portland, OR (booknews.com)

An exciting new edition of a classic text


Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.
Why Group Theory? 1(1)
Finite Groups
2(41)
Groups and representations
2(1)
Example - Z3
3(1)
The regular representation
4(1)
Irreducible representations
5(1)
Transformation groups
6(1)
Application: parity in quantum mechanics
7(1)
Example: S3
8(1)
Example: addition of integers
9(1)
Useful theorems
10(1)
Subgroups
11(2)
Schur's lemma
13(4)
Orthogonality relations
17(3)
Characters
20(5)
Eigenstates
25(1)
Tensor products
26(1)
Example of tensor products
27(2)
Finding the normal modes
29(4)
Symmetries of 2n+1-gons
33(1)
Permutation group on n objects
34(1)
Conjugacy classes
35(2)
Young tableaux
37(1)
Example---our old friend S3
38(1)
Another example---S4
38(1)
Young tableaux and representations of Sn
38(5)
Lie Groups
43(13)
Generators
43(2)
Lie algebras
45(2)
The Jacobi identity
47(1)
The adjoint representation
48(3)
Simple algebras and groups
51(1)
States and operators
52(1)
Fun with exponentials
53(3)
SU(2)
56(12)
J3 eigenstates
56(1)
Raising and lowering operators
57(3)
The standard notation
60(3)
Tensor products
63(1)
J3 values add
64(4)
Tensor Operators
68(11)
Orbital angular momentum
68(1)
Using tensor operators
69(1)
The Wigner-Eckart theorem
70(2)
Example
72(3)
Making tensor operators
75(2)
Products of operators
77(2)
Isospin
79(11)
Charge independence
79(1)
Creation operators
80(2)
Number operators
82(1)
Isospin generators
82(1)
Symmetry of tensor products
83(1)
The deuteron
84(1)
Superselection rules
85(1)
Other particles
86(2)
Approximate isospin symmetry
88(1)
Perturbation theory
88(2)
Roots and Weights
90(8)
Weights
90(1)
More on the adjoint representation
91(1)
Roots
92(1)
Raising and lowering
93(1)
Lots of SU(2)s
93(2)
Watch carefully-this is important!
95(3)
SU(3)
98(5)
The Gell-Mann matrices
98(2)
Weights and roots of SU(3)
100(3)
Simple Roots
103(22)
Positive weights
103(2)
Simple roots
105(3)
Constructing the algebra
108(3)
Dynkin diagrams
111(1)
Example: G2
112(1)
The roots of G2
112(2)
The Cartan matrix
114(1)
Finding all the roots
115(2)
The SU(2)s
117(1)
Constructing the G2 algebra
118(2)
Another example: the algebra C3
120(1)
Fundamental weights
121(2)
The trace of a generator
123(2)
More SU(3)
125(13)
Fundamental representations of SU(3)
125(2)
Constructing the states
127(3)
The Weyl group
130(1)
Complex conjugation
131(1)
Examples of other representations
132(6)
Tensor Methods
138(28)
lower and upper indices
138(1)
Tensor components and wave functions
139(1)
Irreducible representations and symmetry
140(1)
Invariant tensors
141(1)
Clebsch-Gordan decomposition
141(2)
Triality
143(1)
Matrix elements and operators
143(1)
Normalization
144(1)
Tensor operators
145(1)
The dimension of (n, m)
145(1)
The weights of (n, m)
146(6)
Generalization of Wigner-Eckart
152(2)
Tensors for SU(2)
154(2)
Clebsch-Gordan coefficients from tensors
156(1)
Spin s1 + s2 - 1
157(3)
Spin s1 + s2 - k
160(6)
Hypercharge and Strangeness
166(12)
The eight-fold way
166(3)
The Gell-Mann Okubo formula
169(4)
Hadron resonances
173(1)
Quarks
174(4)
Young Tableaux
178(9)
Raising the indices
178(2)
Clebsch-Gordan decomposition
180(3)
SU(3) → SU(2) x U(1)
183(4)
SU(N)
187(11)
Generalized Gell-Mann matrices
187(3)
SU(N) tensors
190(3)
Dimensions
193(1)
Complex representations
194(1)
SU(N) ⊗ SU(M) ∈ SU(N + M)
195(3)
3-D Harmonic Oscillator
198(7)
Raising and lowering operators
198(2)
Angular momentum
200(1)
A more complicated example
200(5)
SU(6) and the Quark Model
205(9)
Including the spin
205(1)
SU(N) ⊗ SU(M) ∈ SU(NM)
206(2)
The baryon states
208(2)
Magnetic moments
210(4)
Color
214(7)
Colored quarks
214(4)
Quantum Chromodynamics
218(1)
Heavy quarks
219(1)
Flavor SU(4) is useless!
219(2)
Constriuent Quarks
221(4)
The nonrelativistic limit
221(4)
Unified Theories and SU(5)
225(12)
Grand unification
225(1)
Parity violation, helicity and handedness
226(2)
Spontaneously broken symmetry
228(1)
Physics of spontaneous symmetry breaking
229(1)
Is the Higgs real?
230(1)
Unification and SU(5)
231(3)
Breaking SU(5)
234(1)
Proton decay
235(2)
The Classical Groups
237(7)
The SO(2n) algebras
237(1)
The SO(2n + 1) algebras
238(1)
The Sp(2n) algebras
239(1)
Quaternions
240(4)
The Classification Theorem
244(11)
II-systems
244(7)
Regular subalgebras
251(2)
Other Subalgebras
253(2)
SO(2n + 1) and Spinors
255(10)
Fundamental weight of SO(2n + 1)
255(4)
Real and pseudo-real
259(2)
Real representations
261(1)
Pseudo-real representations
262(1)
R is an invariant tensor
262(1)
The explicit from for R
262(3)
SO(2n + 2) Spinors
265(5)
Fundamental weights of SO(2n + 2)
265(5)
SU(n) ⊂ SO(2n)
270(12)
Clifford algebras
270(2)
Γm and R as invariant tensors
272(2)
Products of Γs
274(3)
Self-duality
277(2)
Example: SO(10)
279(1)
The SU(n) subalgebra
279(3)
SO(10)
282(9)
SO(10) and SU(4) x SU(2) x SU(2)
282(3)
Spontaneous breaking of SO(10)
285(1)
Breaking SO(10) → SU(5)
285(2)
Breaking SO(10) → SU(3) x SU(2) x U(1)
287(2)
Breaking SO(10) → SU(3) x U(1)
289(1)
Lepton number as a fourth color
289(2)
Automorphisms
291(6)
Outer automorphisms
291(2)
Fun with SO(8)
293(4)
Sp(2n)
297(5)
Weights of SU(n)
297(2)
Tensors for Sp(2n)
299(3)
Odds and Ends
302(9)
Exceptional algebras and octonians
302(2)
E6 unification
304(4)
Breaking E6
308(1)
SU(3) x SU(3) x SU(3) unification
308(1)
Anomalies
309(2)
Epilogue 311(1)
Index 312
Howard Georgi is professor of physics at Harvard University.