Quantum field theory of point particles and strings

By: Hatfield, BrianSeries: Frontiers in physics ; v. 75Publication details: Boca Raton, Florida: CRC Press, [c2018]Description: 734 pISBN: 9780201360790LOC classification: QC174.45 .H29
Contents:
I. Point Particles * Introduction: Phenomenology Overview * First to Second Quantization * Free Scalar Field Theory * Free Spinor Field Theory * Quantization of the Electromagnetic Field * Self-Interacting Scalar Field Theory * Spinor Quantum Electrodynamics * Functional Calculus * Free Fields in the Schrdinger Representation * Interacting Fields in the Schrdinger Representation * Path Integral Representation of Quantum Mechanics * Path Integrals in Free Field Theory * Interacting Fields and Path Integrals * Yang-Mills and Faddeev-Popov * Hiding the Infinities * Renormalization of QED at 1-Loop * The Effective Action Strings II. Strings * Basic Ideas and Classical Theory * First Quantization * The Mathematics of Surfaces * Polykovs Integral: The Partition Function for Genus 0 * Higher-Genus Integrals * Scattering Amplitudes * Noncritical Dimensions * Introduction to Superstrings * Bibliography * Index
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
* Introduction: Phenomenology Overview
* First to Second Quantization
* Free Scalar Field Theory
* Free Spinor Field Theory
* Quantization of the Electromagnetic Field
* Self-Interacting Scalar Field Theory
* Spinor Quantum Electrodynamics
* Functional Calculus
* Free Fields in the Schrdinger Representation
* Interacting Fields in the Schrdinger Representation
* Path Integral Representation of Quantum Mechanics
* Path Integrals in Free Field Theory
* Interacting Fields and Path Integrals
* Yang-Mills and Faddeev-Popov
* Hiding the Infinities
* Renormalization of QED at 1-Loop
* The Effective Action Strings
II. Strings
* Basic Ideas and Classical Theory
* First Quantization
* The Mathematics of Surfaces
* Polykovs Integral: The Partition Function for Genus 0
* Higher-Genus Integrals
* Scattering Amplitudes
* Noncritical Dimensions
* Introduction to Superstrings
* Bibliography
* Index

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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