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By L. Nachbin

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Extra resources for Functional Analysis and Applications

Example text

Basic Ideas of Renormalization . . . . . . . . . . . . . 1 The Effective Mass and the Effective Charge of the Electron . . . . . . . . . . . . . . . . . . . 2 The Counterterms of the Modified Lagrangian . . . 3 The Compensation Principle . . . . . . . . . . . 4 Fundamental Invariance Principles . . . . . . . . 5 Dimensional Regularization of Discrete Algebraic Feynman Integrals . . . . . . . . . . . . . . . 6 Multiplicative Renormalization .

1 The Macroscopic Diffusion Law . . . . . . . . . 2 Einstein’s Key Formulas for the Brownian Motion . 3 The Random Walk of Particles . . . . . . . . . . 4 The Rigorous Wiener Path Integral . . . . . . . . 5 The Feynman–Kac Formula . . . . . . . . . . . 12 Weyl Quantization . . . . . . . . . . . . . . . . . . 1 The Formal Moyal Star Product . . . . . . . . . 3 Weyl Ordering . . . . . . . . . . . . . . . . . 4 Operator Kernels .

1 The Photon Propagator . . . . . . . . . . . . . 2 The Electron Propagator . . . . . . . . . . . . 3 The Vertex Correction and the Ward Identity . . . 4 The Counterterms of the Lagrangian and the Compensation Principle . . . . . . . . . . . . . . . . . . . . . . . 5 Application to Physical Problems . . . . . . . . . . . . 1 Radiative Correction of the Coulomb Potential . . . 2 The Anomalous Magnetic Moment of the Electron .

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