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Elements of Advanced Quantum Theory - J. M. Ziman

Elements of Advanced Quantum Theory


Published: 30th May 1975
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This is a textbook of advanced quantum theory for graduate students and research workers which gives a connected mathematical derivation of the important results, concentrating on the central ideas without burdening the exposition with elaborate detail or unnecessary rigour, and explains, in the simplest possible terms, the symbols and concepts which frequently confront the active research worker in solid state, nuclear and high-energy physics, and in theoretical chemistry. Professor Ziman brings to his task the sympathetic guidance of a lecturer who has not forgotten the difficulties that he himself had to surmount in mastering his subject.

'An outstanding book ... Essential for all libraries and probably for most physicists.' Choice 'The reader will find an easy and often delightful path to the understanding of the rather sophisticated concepts.' P. Roman, Mathematical Reviews 'An unqualified success.' S. M. Blinder, Journal of the American Chemical Society

Prefacep. v
The simple harmonic oscillatorp. 1
Annihilation and creation operatorsp. 3
Coupled oscillators: the linear chainp. 5
Three-dimensional lattices and vector fieldsp. 9
The continuum limitp. 12
Classical field theoryp. 14
Second quantizationp. 18
Klein--Gordon equationp. 21
Sources of a field, and interactions between fieldsp. 22
Example: Rayleigh scattering of phononsp. 24
Example: Yukawa forcep. 26
Charged bosonsp. 28
Occupation-number representationp. 32
Annihilation and creation operators: anticommutationp. 33
Second quantizationp. 36
Scattering: connection with statistical mechanicsp. 39
Interactions between particles: momentum conservationp. 41
Fermion--boson interactionp. 43
Holes and antiparticlesp. 48
Perturbation theory
The Brillouin--Wigner seriesp. 53
The Heisenberg representationp. 56
Interaction representationp. 60
Time--integral expansion seriesp. 62
S-matrixp. 64
S-matrix expansion: algebraic theoryp. 67
Diagrammatic representationp. 74
Momentum representationp. 80
The physical vacuump. 86
Dyson's equation and renormalizationp. 90
Green functions
The density matrixp. 94
Equation of motion of density operatorp. 98
Ensembles in thermal equilibriump. 99
The Kubo formulap. 101
The one-particle Green functionp. 104
Energy--momentum representationp. 107
Evaluation of Green functionsp. 110
Two-particle Green functionsp. 112
The hierarchy of Green functionsp. 116
Time-independent Green functionsp. 117
Matrix representation of the Green functionp. 120
Space representation of time-independent Green functionp. 122
The Born seriesp. 124
The T-matrixp. 127
Example: impurity states in a metalp. 129
Some aspects of the many-body problem
Quantum properties of macroscopic systemsp. 135
Statistical methods: the Thomas--Fermi approximationp. 136
Hartree self-consistent fieldp. 138
The Hartree--Fock methodp. 140
Diagrammatic interpretation of Hartree--Fock theoryp. 143
The Brueckner methodp. 146
The dielectric response functionp. 148
Spectral representation of dielectric functionp. 150
Diagrammatic interpretation of dielectric screeningp. 154
The random phase approximationp. 158
The Landau theory of Fermi liquidsp. 162
The dilute Bose gasp. 167
The superconducting statep. 170
Relativistic formulations
Lorentz invariancep. 175
Relativistic electromagnetic theoryp. 177
The wave equation and gauge invariancep. 180
Quantization of relativistic fieldsp. 183
Spinorsp. 187
The Dirac equationp. 191
The Dirac matricesp. 193
Quantization of the Dirac fieldp. 196
Interactions between relativistic fieldsp. 199
Relativistic kinematicsp. 203
The analytic S-matrixp. 207
The algebra of symmetry
Symmetry operationsp. 213
Representationsp. 215
Regular representations of finite groupsp. 219
The orthogonality theoremp. 222
Character and classp. 225
Product groups and representationsp. 230
Translation groupsp. 235
Continuous groupsp. 237
The rotation groupp. 241
Irreducible representations of the rotation groupp. 244
Spinor representationsp. 247
SU(2)p. 249
SU(3)p. 254
Indexp. 259
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521099493
ISBN-10: 0521099498
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 284
Published: 30th May 1975
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 15.88  x 1.91
Weight (kg): 0.43