Foundations of Quantum Field Theory. Klaus D Rothe

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СКАЧАТЬ href="#ulink_f5b61fa6-8eda-5a8c-bd2b-c4f3a60a762f"> 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 СКАЧАТЬ