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Physics of Quantum Fields 2000 ed. [Kõva köide]

  • Formaat: Hardback, 271 pages, kõrgus x laius: 235x155 mm, kaal: 1300 g, XIV, 271 p., 1 Hardback
  • Sari: Graduate Texts in Contemporary Physics
  • Ilmumisaeg: 28-Dec-1999
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387989099
  • ISBN-13: 9780387989099
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  • Formaat: Hardback, 271 pages, kõrgus x laius: 235x155 mm, kaal: 1300 g, XIV, 271 p., 1 Hardback
  • Sari: Graduate Texts in Contemporary Physics
  • Ilmumisaeg: 28-Dec-1999
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387989099
  • ISBN-13: 9780387989099
A gentle introduction to the physics of quantized fields and many-body physics. Based on courses taught at the University of Illinois, it concentrates on the basic conceptual issues that many students find difficult, and emphasizes the physical and visualizable aspects of the subject. While the text is intended for students with a wide range of interests, many of the examples are drawn from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics, while the Feynman path integral is introduced in the second half where it is seen as indispensable for understanding the connection between renormalization and critical as well as non-perturbative phenomena.

This book provides an introduction to the physics of quantized fields and many-body physics. It concentrates on the basic conceptual issues that many find difficult, and emphasizes the physical and visualizable aspects, employing examples from condensed matter physics because of the tangible character of such systems. The first part of the book uses the Hamiltonian operator language of traditional quantum mechanics to treat simple field theories and related topics. The Feynman path integral is introduced in the second half.

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Springer Book Archives
Preface vi
Discrete Systems
1(11)
One-Dimensional Harmonic Crystal
1(6)
Normal Modes
1(3)
Harmonic Oscillator
4(1)
Annihilation and Creation Operators for Normal Modes
5(2)
Continuum Limit
7(5)
Sums and Integrals
7(1)
Continuum Fields
8(4)
Relativistic Scalar Fields
12(13)
Conventions
12(1)
The Klein-Gordon Equation
13(5)
Relativistic Normalization
14(2)
An Inner Product
16(1)
Complex Scalar Fields
17(1)
Symmetries and Noether's Theorem
18(7)
Internal Symmetries
18(3)
Space-Time Symmetries
21(4)
Perturbation Theory
25(12)
Interactions
25(1)
Perturbation Theory
26(4)
Interaction Picture
26(1)
Propagators and Time-Ordered Products
27(3)
Wick's Theorem
30(7)
Normal Products
30(1)
Wick's Theorem
30(2)
Applications
32(5)
Feynman Rules
37(11)
Diagrams
37(6)
Diagrams in Space-time
37(4)
Diagrams in Momentum Space
41(2)
Scattering Theory
43(5)
Cross-Sections
44(3)
Decay of an Unstable Particle
47(1)
Loops, Unitarity, and Analyticity
48(14)
Unitarity of the S Matrix
48(3)
The Analytic S Matrix
51(5)
Origin of Analyticity
51(1)
Unitarity and Branch Cuts
52(2)
Resonances, Widths, and Lifetimes
54(2)
Some Loop Diagrams
56(6)
Wick Rotation
56(2)
Feynman Parameters
58(1)
Dimensional Regularization
59(3)
Formal Developments
62(10)
Gell-Mann Low Theorem
62(2)
Lehmann-Kallen Spectral Representation
64(3)
LSZ Reduction Formulae
67(5)
Amputation of External Legs
67(1)
In and Out States and Fields
68(3)
Borcher's Classes
71(1)
Fermions
72(11)
Dirac Equation
72(2)
Spinors, Tensors, and Currents
74(1)
Field Bilinears
74(1)
Conservation Laws
75(1)
Holes and the Dirac Sea
75(4)
Positive and Negative Energies
75(3)
Holes
78(1)
Quantization
79(4)
Normal and Time-Ordered Products
81(2)
QED
83(14)
Quantizing Maxwell's Equations
83(5)
Hamiltonian Formalism
83(1)
Axial Gauge
84(1)
Lorentz Gauge
85(3)
Feynman Rules for QED
88(4)
Moøller Scattering
90(2)
Ward Identity and Gauge Invariance
92(5)
The Ward Identity
92(1)
Applications
93(4)
Electrons in Solids
97(20)
Second Quantization
97(3)
Fermi Gas and Fermi Liquid
100(14)
One-Particle Density Matrix
100(3)
Linear Response
103(1)
Diagram Approach
104(2)
Applications
106(8)
Electrons and Phonons
114(3)
Nonrelativistic Bosons
117(19)
The Boson Field
117(1)
Spontaneous Symmetry Breaking
118(4)
Dilute Bose Gas
122(9)
Bogoliubov Transfomation
122(3)
Field Equations
125(1)
Quantization
126(2)
Landau Criterion for Superfluidity
128(1)
Normal and Superfluid Densities
129(2)
Charged Bosons
131(5)
Gross-Pitaevskii Equation
131(1)
Vortices
132(2)
Connection with Fluid Mechanics
134(2)
Finite Temperature
136(7)
Partition Functions
136(1)
Worldlines
137(3)
Matsubara Sums
140(3)
Path Integrals
143(15)
Quantum Mechanics of a Particle
143(5)
Real Time
143(3)
Euclidean Time
146(2)
Gauge Invariance and Operator Ordering
148(2)
Correlation Functions
150(2)
Fields
152(1)
Gaussian Integrals and Free Fields
153(3)
Real Fields
153(2)
Complex Fields
155(1)
Perturbation Theory
156(2)
Functional Methods
158(13)
Generating Functionals
158(8)
Effective Action
161(5)
Ward Identities
166(5)
Goldstone's Theorem
167(4)
Path Integrals for Fermions
171(14)
Berezin Integrals
171(6)
A Simple Supersymmetry
174(3)
Fermionic Coherent States
177(2)
Superconductors
179(6)
Effective Action
181(4)
Lattice Field Theory
185(16)
Boson Fields
185(4)
Random Walks
189(2)
Interactions and Bose Condensation
191(4)
Rotational Invariance
192(3)
Lattice Fermions
195(6)
No Chiral Lattice Fermions
200(1)
The Renormalization Group
201(12)
Transfer Matrices
202(4)
Continuum Limit
204(1)
Two-Dimensional Ising Model
205(1)
Block Spins and Renormalization Group
206(7)
Correlation Functions
212(1)
Fields and Renormalization
213(20)
The Free-Field Fixed Point
213(2)
The Gaussian Model
215(4)
General Method
219(1)
Nonlinear σ Model
220(9)
Renormalizing
225(3)
Solution of the RGE
228(1)
Renormalizing λφv;4
229(4)
Large N Expansions
233(13)
O(N) Linear σ-Model
233(4)
Large N Expansions
237(9)
Linear vs. Nonlinear σ-Models
241(5)
A Relativistic State Normalization
246(2)
B The General Commutator
248(2)
C Dimensional Regularization
250(4)
C.1 Analytic Continuation and Integrals
250(2)
C.2 Propagators
252(2)
D Spinors and the Principle of the Sextant
254(4)
D.1 Constructing the γ-Matrices
254(1)
D.2 Basic Theorem
255(1)
D.3 Chirality
256(1)
D.4 Spin(2N), Pin(2N), and SU(N) ⊂ SO(2N)
257(1)
E Indefinite Metric
258(3)
F Phonons and Momentum
261(3)
G Determinants in Quantum Mechanics
264(3)
Index 267