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Finite Quantum Electrodynamics - G. Scharf

Finite Quantum Electrodynamics

The Causal Approach

(Autor)

Buch | Softcover
X, 410 Seiten
2012 | 2nd ed. 1995. Softcover reprint of the original 2nd ed. 1995
Springer Berlin (Verlag)
978-3-642-63345-4 (ISBN)
CHF 74,85 inkl. MwSt
In this textbook for graduate students in physics the author carefully analyses the role of causality in Q.E.D. This new approach avoids ultraviolet divergences, so that the detailed calculations of scattering processes and proofs can be carried out in a mathematically rigorous manner. Significant themes such as renormalizability, gauge invariance, unitarity, renormalization group, interacting fields and axial anomalies are discussed. The extension of the methods to non-abelian gauge theories is briefly described.
The book differs considerably from its first edition: Chap. 3 on Causal Perturbation Theory was completely rewritten and Chap. 4 on Properties of the S-Matrix and Chap. 5 on Other Electromagnetic Couplings are new.

0. Preliminaries.- 0.0 Historical Introduction.- 0.1 Minkowski Space and the Lorentz Group.- 0.2 Tensors in Minkowski Space.- 0.3 Some Topics of Scattering Theory.- 0.4 Problems.- 1. Relativistic Quantum Mechanics.- 1.1 Spinor Representations of the Lorentz Group.- 1.2 Invariant Field Equations.- 1.3 Algebraic Properties of the Dirac Equation.- 1.4 Discussion of the Free Dirac Equation.- 1.5 Gauge Invariance and Electromagnetic Fields.- 1.6 The Hydrogen Atom.- 1.7 Problems.- 2. Field Quantization.- 2.1 Second Quantization in Fock Space.- 2.2 Quantization of the Dirac Field.- 2.3 Discussion of the Commutation Functions.- 2.4 The Scattering Operator (S-Matrix) in Fock Space.- 2.5 Perturbation Theory.- 2.6 Electron Scattering.- 2.7 Pair Production.- 2.8 The Causal Phase of the S-Matrix.- 2.9 Non-Perturbative Construction of the Causal Phase.- 2.10 Vacuum Polarization.- 2.11 Quantization of the Radiation Field.- 2.12 Problems.- 3. Causal Perturbation Theory.- 3.1 The Method of Epstein and Glaser.- 3.2 Splitting of Causal Distributions.- 3.3 Application to QED.- 3.4 Electron Scattering (Moeller Scattering).- 3.5 Electron-Photon Scattering (Compton Scattering).- 3.6 Vacuum Polarization.- 3.7 Self-Energy.- 3.8 Vertex Function: Causal Distribution.- 3.9 Vertex Function: Retarded Distribution.- 3.10 Form Factors.- 3.11 Adiabatic Limit.- 3.12 Charged Particles in Perturbative QED.- 3.13 Charge Normalization.- 3.14 Problems.- 4. Properties of the S-Matrix.- 4.1 Vacuum Graphs.- 4.2 Operator Character of the S-Matrix.- 4.3 Normalizability of QED.- 4.4 Discrete Symmetries.- 4.5 Poincaré Covariance.- 4.6 Gauge Invariance and Ward Identities.- 4.7 Unitarity.- 4.8 Renormalization Group.- 4.9 Interacting Fields and Operator Products.- 4.10 Field Equations.- 4.11 Problems.- 5. OtherElectromagnetic Couplings.- 5.1 Scalar QED: Basic Properties.- 5.2 Scalar QED: Gauge Invariance.- 5.3 Axial Anomalies.- 5.4 (2+1)-Dimensional QED: Vacuum Polarization.- 5.5 (2+1)-Dimensional QED: Mass Generation.- 5.6 Problems.- 6. Epilogue: Non-Abelian Gauge Theories.- Appendices.- A: The Hydrogen Atom According to the Schrödinger Equation.- B: Regularly Varying Functions.- C: Spence Functions.- D: Grassmann Test Functions.- Bibliographical Notes.

From the reviews: "In the summary on the back cover the unheard-of statement appears that now the first (mathematically) rigorous textbook on Quantum Electrodynamics was on hand. ... In fact, "Finite Quantum Electrodynamics" does justice to this claim. And, in addition, in a pregnant, lifely form. On 220 pages G. Scharf (Zurich) succeeds in presenting a concise description of QED ... As promised, only finite quantities appear ... In Russia I often feel frustrated that I studied Latin in school and Russian was not offered. Now I have the same feeling after reading Scharf's book. I studied the wrong grammar up to now." #Translated from a review by Thomas Schücker in Physik in unserer Zeit#1

From the reviews: "In the summary on the back cover the unheard-of statement appears that now the first (mathematically) rigorous textbook on Quantum Electrodynamics was on hand. ... In fact, "Finite Quantum Electrodynamics" does justice to this claim. And, in addition, in a pregnant, lifely form. On 220 pages G. Scharf (Zurich) succeeds in presenting a concise description of QED ... As promised, only finite quantities appear ... In Russia I often feel frustrated that I studied Latin in school and Russian was not offered. Now I have the same feeling after reading Scharf's book. I studied the wrong grammar up to now." #Translated from a review by Thomas Schücker in Physik in unserer Zeit#1

Erscheint lt. Verlag 13.11.2012
Reihe/Serie Theoretical and Mathematical Physics
Zusatzinfo X, 410 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 599 g
Themenwelt Naturwissenschaften Physik / Astronomie Quantenphysik
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Dirac equation • Minkowski space • Quantenelektrodynamik • quantum mechanics • Renormalization Group • scattering theory • Second Quantization
ISBN-10 3-642-63345-5 / 3642633455
ISBN-13 978-3-642-63345-4 / 9783642633454
Zustand Neuware
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