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Foundations Of Quantum Field Theory [Pehme köide]

(Univ Heidelberg, Germany)
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Foundations Of Quantum Field TheorySuurem pilt
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"Based on a two-semester course held at the University of Heidelberg, Germany, this book provides an adequate resource for the lecturer and the student. The contents are primarily aimed at graduate students who wish to learn about the fundamental concepts behind constructing a Relativistic Quantum Theory of particles and fields. So it provides a comprehensive foundation for the extension to Quantum Chromodynamics and Weak Interactions, that are not included in this book"--
Preface vii
1 The Principles of Quantum Physics
1(8)
1.1 Principles shared by QM and QFT
1(2)
1.2 Principles of NRQM not shared by QFT
3(6)
2 Lorentz Group and Hilbert Space
9(18)
2.1 Defining properties of Lorentz transformations
9(3)
2.2 Classification of Lorentz transformations
12(2)
2.3 Lie algebra of the Lorentz group
14(3)
2.4 Finite irreducible representation of L\
17(3)
2.5 Transformation properties of massive 1-particle states
20(3)
2.6 Transformation properties of zero-mass 1-particle states
23(4)
3 Search for a Relativistic Wave Equation
27(9)
3.1 A relativistic Schrodinger equation
27(2)
3.2 Difficulties with the wave equation
29(3)
3.3 The Klein-Gordon equation
32(1)
3.4 KG equation in the presence of an electromagnetic field
33(3)
4 The Dirac Equation
36(18)
4.1 Dirac spinors in the Dirac and Weyl representations
36(8)
4.2 Properties of the Dirac spinors
44(1)
4.3 Properties of the γ-matrices
45(2)
4.4 Zero-mass, spin = 1/2 fields
47(4)
4.5 Majorana fermions
51(3)
5 The Free Maxwell Field
54(4)
5.1 The radiation field in the Lorentz gauge
54(2)
5.2 The radiation field in the Coulomb gauge
56(2)
6 Quantum Mechanics of Dirac Particles
58(16)
6.1 Probability interpretation
58(3)
6.2 Non-relativistic limit
61(1)
6.3 Negative-energy solutions and localization
62(2)
6.4 The Klein Paradox
64(3)
6.5 Foldy-Wouthuysen Transformation
67(7)
7 Second Quantization
74(16)
7.1 Fock-space representation of fields
74(8)
7.2 Commutation relations
82(3)
7.3 P, C, T from equations of motion
85(3)
7.4 P, C, T in second quantization
88(2)
8 Canonical Quantization
90(17)
8.1 Lagrangian formulation and Euler-Lagrange equations
90(5)
8.2 Canonical quantization: unconstrained systems
95(3)
8.3 Canonical quantization: constrained systems
98(3)
8.4 QED as a constrained system
101(6)
9 Global Symmetries and Conservation Laws
107(10)
9.1 Noether's Theorem
107(3)
9.2 Internal symmetries
110(2)
9.3 Translational invariance
112(2)
9.4 Lorentz transformations
114(3)
10 The Scattering Matrix
117(17)
10.1 The S-matrix and T-matrix
118(4)
10.2 Differential cross-section
122(5)
10.3 LSZ reduction formula
127(7)
11 Perturbation Theory
134(32)
11.1 Interaction picture and U-matrix
134(2)
11.2 Interaction picture representation of Green functions
136(3)
11.3 Wick theorems
139(3)
11.4 2-point functions
142(6)
11.5 Feynman Diagrams for QED
148(5)
11.6 Furry's theorem
153(1)
11.7 Going over to momentum space
154(2)
11.8 Momentum space Feynman rules for QED
156(1)
11.9 Moeller scattering
157(3)
11.10 The Moeller differential cross-section
160(3)
11.11 Compton scattering
163(3)
12 Parametric Representation of a General Diagram
166(13)
12.1 Cutting rules for a general diagram
166(6)
12.2 An alternative approach to cutting rules
172(3)
12.3 4-point function in the ladder approximation
175(4)
13 Functional Methods
179(34)
13.1 The Generating Functional
180(1)
13.2 Schwinger's Construction of Z[ j]
180(4)
13.3 Feynman Path-Integral
184(5)
13.4 Path-integral representation of correlators in QM
189(5)
13.5 Feynman path-integral representation in QFT
194(4)
13.6 Path-Integral for Grassman-valued fields
198(6)
13.7 Extension to Field Theory
204(2)
13.8 Mathews-Salam representation of QED generating functional
206(3)
13.9 Faddeev-Popov quantization and a-gauges
209(4)
14 Dyson-Schwinger Equation
213(7)
14.1 Classification of Feynman Diagrams
213(2)
14.2 Basic building blocks of QED
215(3)
14.3 Dyson-Schwinger Equations
218(2)
15 Regularization of Feynman Diagrams
220(16)
15.1 Pauli-Villars and dimensional regularization
220(16)
15.1.1 Electron self-energy
222(4)
15.1.2 Photon vacuum polarization
226(5)
15.1.3 The vertex function
231(5)
16 Renormalization
236(37)
16.1 The principles of renormalization
237(3)
16.2 Renormalizability of QED
240(6)
16.2.1 Fermion 2-point function
242(2)
16.2.2 Photon 2-point function
244(1)
16.2.3 Vertex function
245(1)
16.3 Ward-Takahashi Identity and overlapping divergences
246(5)
16.4 1-loop renormalization in QED
251(4)
16.5 Composite operators and Wilson expansion
255(1)
16.6 Criteria for renormalizability
256(4)
16.7 Taylor subtraction
260(3)
16.8 Bogoliubov's recursion formula
263(1)
16.9 Overlapping divergences
264(3)
16.10 Dispersion relations: a brief view
267(6)
17 Broken Scale Invariance and Callan-Symanzik Equation
273(30)
17.1 Scale transformations
274(3)
17.2 Unrenormalized Ward identities of broken scale invariance
277(3)
17.3 Broken scale invariance and renormalized Ward identities
280(3)
17.4 Weinberg's Theorem
283(3)
17.5 Solution of CS equation in the deep euclidean region
286(4)
17.6 Asymptotic behaviour of γ and zeros of the β-function
290(3)
17.7 Perturbative calculation of β(g) and γ(g) inφ4 theory
293(5)
17.8 QED β-function and anomalous dimension
298(1)
17.9 QED β-function and leading log summation
299(2)
17.10 Infrared fix point of QED and screening of charge
301(2)
18 Renormalization Group
303(8)
18.1 The Renormalization Group equation
303(6)
18.2 Asymptotic solution of RG equation
309(2)
19 Spontaneous Symmetry Breaking
311(10)
19.1 The basic idea
311(2)
19.2 More about spontaneous symmetry breaking
313(3)
19.3 The Goldstone Theorem
316(2)
19.4 Realization of Goldstone Theorem in QFT
318(3)
20 Effective Potentials
321(14)
20.1 Generating functional of proper functions
321(3)
20.2 The effective potential
324(1)
20.3 The 1-loop effective potential of 04-theory
325(2)
20.4 WKB approach to the effective potential
327(2)
20.5 The effective potential and SSB
329(6)
Index 335