Quantum Field Theory in Condensed Matter Physics

כריכה קדמית
Springer Science & Business Media, 20 בספט׳ 1999 - 206 עמודים
Why is quantum field theory of condensed matter physics necessary? Condensed matter physics deals with a wide variety of topics, ranging from gas to liquids and solids, as well as plasma, where owing to the inter play between the motions of a tremendous number of electrons and nuclei, rich varieties of physical phenomena occur. Quantum field theory is the most appropriate "language", to describe systems with such a large number of de grees of freedom, and therefore its importance for condensed matter physics is obvious. Indeed, up to now, quantum field theory has been succesfully ap plied to many different topics in condensed matter physics. Recently, quan tum field theory has become more and more important in research on the electronic properties of condensed systems, which is the main topic of the present volume. Up to now, the motion of electrons in solids has been successfully de scribed by focusing on one electron and replacing the Coulomb interaction of all the other electrons by a mean field potential. This method is called mean field theory, which made important contributions to the explanantion of the electronic structure in solids, and led to the classification of insulators, semiconductors and metals in terms of the band theory. It might be said that also the present achievements in the field of semiconductor technology rely on these foundations. In the mean field approximation, effects that arise due to the correlation of the motions of many particles, cannot be described.
 

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תוכן

1 Review of Quantum Mechanics and Basic Principles of Field Theory
1
Second Quantization
12
13 The Variation Principle and the Noether Theorem
18
14 Quantization of the Electromagnetic Field
23
2 Quantization with Path Integral Methods
27
22 The Path Integral for Bosons
37
23 The Path Integral for Fermions
42
24 The Path Integral for the Gauge Field
45
42 The Bogoliubov Theory of Superfluidity
102
5 Problems Related to Superconductivity
113
The Josephson Junction
133
53 The SuperconductorInsulator Phase Transition in Two Dimensions and the Quantum Vortices
146
6 Quantum Hall Liquid and the ChernSimons Gauge Field
161
62 Effective Theory of a Quantum Hall Liquid
167
63 The Derivation of the Laughlin Wave Function
186
Appendix
193

25 The Path Integral for the Spin System
47
3 Symmetry Breaking and Phase Transition
51
32 The Goldstone Mode
60
33 Kosterlitz Thouless Transition
68
34 Lattice Gauge Theory and the Confinement Problem
78
4 Simple Examples for the Application of Field Theory
91
B Functionals and the Variation Principle
195
С Quantum Statistical Mechanics
199
References
201
Index
205
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