Quantum field theory of point particles and strings

By: Brian HatfieldSeries: Frontiers in physics ; vol. 75Publication details: Boca Raton, Florida: CRC Press, [c2018]Description: 734 pISBN: 9780201360790Subject(s): Mathematics & StatisticsLOC classification: QC174.45.H29
Contents:
I. Point Particles 1. Introduction: Phenomenology Overview 2. First to Second Quantization 3. Free Scalar Field Theory 4. Free Spinor Field Theory 5. Quantization of the Electromagnetic Field 6. Self-Interacting Scalar Field Theory 7. Spinor Quantum Electrodynamics 8. Functional Calculus 9. Free Fields in the Schrdinger Representation 10. Interacting Fields in the Schrdinger Representation 11. Path Integral Representation of Quantum Mechanics 12. Path Integrals in Free Field Theory 13. Interacting Fields and Path Integrals 14. Yang-Mills and Faddeev-Popov 15. Hiding the Infinities 16. Renormalization of QED at 1-Loop 17. The Effective Action Strings II. Strings 18. Basic Ideas and Classical Theory 19. First Quantization 20. The Mathematics of Surfaces 21. Polykovs Integral: The Partition Function for Genus 0 22. Higher-Genus Integrals 23. Scattering Amplitudes 24. Noncritical Dimensions 25. Introduction to Superstrings
Summary: The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string. The treatment is most detailed in the path integral representation where the object of interest, the partition function, is a sum over random surfaces. The relevant mathematics of Riemann surfaces is covered. Superstrings are briefly introduced, and the sum over genus 0 supersurfaces is computed.The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory.--- summary provided by the publisher
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I. Point Particles
1. Introduction: Phenomenology Overview
2. First to Second Quantization
3. Free Scalar Field Theory
4. Free Spinor Field Theory
5. Quantization of the Electromagnetic Field
6. Self-Interacting Scalar Field Theory
7. Spinor Quantum Electrodynamics
8. Functional Calculus
9. Free Fields in the Schrdinger Representation
10. Interacting Fields in the Schrdinger Representation
11. Path Integral Representation of Quantum Mechanics
12. Path Integrals in Free Field Theory
13. Interacting Fields and Path Integrals
14. Yang-Mills and Faddeev-Popov
15. Hiding the Infinities
16. Renormalization of QED at 1-Loop
17. The Effective Action Strings

II. Strings
18. Basic Ideas and Classical Theory
19. First Quantization
20. The Mathematics of Surfaces
21. Polykovs Integral: The Partition Function for Genus 0
22. Higher-Genus Integrals
23. Scattering Amplitudes
24. Noncritical Dimensions
25. Introduction to Superstrings

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string. The treatment is most detailed in the path integral representation where the object of interest, the partition function, is a sum over random surfaces. The relevant mathematics of Riemann surfaces is covered. Superstrings are briefly introduced, and the sum over genus 0 supersurfaces is computed.The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory.--- summary provided by the publisher

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