Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 8
ОглавлениеContents
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
3.4KG equation in the presence of an electromagnetic field
4.1Dirac spinors in the Dirac and Weyl representations
4.2Properties of the Dirac spinors
4.3Properties of the γ-matrices
5.1The radiation field in the Lorentz gauge
5.2The radiation field in the Coulomb gauge
6Quantum Mechanics of Dirac Particles
6.3Negative-energy solutions and localization
6.5Foldy–Wouthuysen Transformation
7.1Fock-space representation of fields
7.3P, C, T from equations of motion
7.4P, C, T in second 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
10.2Differential cross-section
11.1Interaction picture and U-matrix
11.2Interaction picture representation of Green functions
11.7Going over to momentum space
11.8Momentum space Feynman rules for QED
11.10The Moeller differential cross-section
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
13.2Schwinger’s Construction of
13.4Path-integral representation of correlators in QM
13.5Feynman path-integral representation in QFT
13.6Path-Integral for Grassman-valued fields
13.8Mathews–Salam representation of QED generating functional
13.9Faddeev–Popov quantization and a-gauges
14.1Classification of Feynman Diagrams
14.2Basic building blocks of QED
15Regularization of Feynman Diagrams
15.1Pauli–Villars and dimensional regularization
15.1.2Photon vacuum polarization
16.1The principles of renormalization
16.2.1Fermion 2-point function
16.3Ward–Takahashi Identity and overlapping divergences
16.41-loop renormalization in QED
16.5Composite operators and Wilson expansion
16.6Criteria for renormalizability
16.8Bogoliubov’s recursion formula
16.10Dispersion relations: a brief view
17Broken Scale Invariance and Callan–Symanzik Equation
17.2Unrenormalized Ward identities of broken scale invariance
17.3Broken scale invariance and renormalized Ward identities
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
18.1The Renormalization Group equation
18.2Asymptotic solution of RG equation
19Spontaneous Symmetry Breaking
19.2More about spontaneous symmetry breaking
19.4Realization of Goldstone Theorem in QFT
20.1Generating functional of proper functions
20.3The 1-loop effective potential of ϕ4-theory
20.4WKB approach to the effective potential
