Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 8

Contents

Preface

1The Principles of Quantum Physics

1.1Principles shared by QM and QFT

1.2Principles of NRQM not shared by QFT

2Lorentz Group and Hilbert Space

2.1Defining properties of Lorentz transformations

2.2Classification of Lorentz transformations

2.3Lie algebra of the Lorentz group

2.4Finite irreducible representation of

2.5Transformation properties of massive 1-particle states

2.6Transformation properties of zero-mass 1-particle states

3Search for a Relativistic Wave Equation

3.1A relativistic Schrödinger equation

3.2Difficulties with the wave equation

3.3The Klein–Gordon equation

3.4KG equation in the presence of an electromagnetic field

4The Dirac Equation

4.1Dirac spinors in the Dirac and Weyl representations

4.2Properties of the Dirac spinors

4.3Properties of the γ-matrices

4.4Zero-mass, spin = fields

4.5Majorana fermions

5The Free Maxwell Field

5.1The radiation field in the Lorentz gauge

5.2The radiation field in the Coulomb gauge

6Quantum Mechanics of Dirac Particles

6.1Probability interpretation

6.2Non-relativistic limit

6.3Negative-energy solutions and localization

6.4The Klein Paradox

6.5Foldy–Wouthuysen Transformation

7Second Quantization

7.1Fock-space representation of fields

7.2Commutation relations

7.3P, C, T from equations of motion

7.4P, C, T in second quantization

8Canonical Quantization

8.1Lagrangian formulation and Euler–Lagrange equations

8.2Canonical quantization: unconstrained systems

8.3Canonical quantization: constrained systems

8.4QED as a constrained system

9Global Symmetries and Conservation Laws

9.1Noether’s Theorem

9.2Internal symmetries

9.3Translational invariance

9.4Lorentz transformations

10The Scattering Matrix

10.1The S-matrix and T-matrix

10.2Differential cross-section

10.3LSZ reduction formula

11Perturbation Theory

11.1Interaction picture and U-matrix

11.2Interaction picture representation of Green functions

11.3Wick theorems

11.42-point functions

11.5Feynman Diagrams for QED

11.6Furry’s theorem

11.7Going over to momentum space

11.8Momentum space Feynman rules for QED

11.9Moeller scattering

11.10The Moeller differential cross-section

11.11Compton scattering

12Parametric Representation of a General Diagram

12.1Cutting rules for a general diagram

12.2An alternative approach to cutting rules

12.34-point function in the ladder approximation

13Functional Methods

13.1The Generating Functional

13.2Schwinger’s Construction of

13.3Feynman Path-Integral

13.4Path-integral representation of correlators in QM

13.5Feynman path-integral representation in QFT

13.6Path-Integral for Grassman-valued fields

13.7Extension to Field Theory

13.8Mathews–Salam representation of QED generating functional

13.9Faddeev–Popov quantization and a-gauges

14Dyson–Schwinger Equation

14.1Classification of Feynman Diagrams

14.2Basic building blocks of QED

14.3Dyson–Schwinger Equations

15Regularization of Feynman Diagrams

15.1Pauli–Villars and dimensional regularization

15.1.1Electron self-energy

15.1.2Photon vacuum polarization

15.1.3The vertex function

16Renormalization

16.1The principles of renormalization

16.2Renormalizability of QED

16.2.1Fermion 2-point function

16.2.2Photon 2-point function

16.2.3Vertex function

16.3Ward–Takahashi Identity and overlapping divergences

16.41-loop renormalization in QED

16.5Composite operators and Wilson expansion

16.6Criteria for renormalizability

16.7Taylor subtraction

16.8Bogoliubov’s recursion formula

16.9Overlapping divergences

16.10Dispersion relations: a brief view

17Broken Scale Invariance and Callan–Symanzik Equation

17.1Scale transformations

17.2Unrenormalized Ward identities of broken scale invariance

17.3Broken scale invariance and renormalized Ward identities

17.4Weinberg’s Theorem

17.5Solution of CS equation in the deep euclidean region

17.6Asymptotic behaviour of r and zeros of the β-function

17.7Perturbative calculation of β(g) and γ(g) in ϕ⁴ theory

17.8QED β-function and anomalous dimension

17.9QED β-function and leading log summation

17.10Infrared fix point of QED and screening of charge

18Renormalization Group

18.1The Renormalization Group equation

18.2Asymptotic solution of RG equation

19Spontaneous Symmetry Breaking

19.1The basic idea

19.2More about spontaneous symmetry breaking

19.3The Goldstone Theorem

19.4Realization of Goldstone Theorem in QFT

20Effective Potentials

20.1Generating functional of proper functions

20.2The effective potential

20.3The 1-loop effective potential of ϕ⁴-theory

20.4WKB approach to the effective potential

20.5The effective potential and SSB

Index