“a pedagogic masterpiece”
This book and this website aim to make learning, and teaching, quantum field theory (QFT) easier, and thus, more efficient and fulfilling.
Both the book and the website are products of extensive student input, incorporate innovative teaching methodologies, and avoid conciseness in favor of elaborate explanations. Every step-by-small-step is included in derivations, and big picture, conceptual overviews (called “wholeness charts”) are provided at every level.
Student Comments about This Book/Website
“[This] book ... makes quantum field theory much easier to understand!"
“… a godsend for the students of QFT.”
“Exactly what I was looking for. I've been struggling to find meaningful explanations of these concepts"
“provided the lucid, yet rigorous understanding I had always yearned for”
“..opened a whole new world for me - the world of proper understanding without undue struggle, misery and despondence.”
“a fantastic introduction to QFT”
“BY FAR the most readable QFT book written I’ve seen.”
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“If your book had been available earlier, I would have done a lot better in the class.”
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Preface (summarizes pedagogic principles employed)
Second edition released. See Information on 2nd Edition
Booklet with solutions to problems in the text released. See problem solutions booklet.
Contents of the Book
CHAPS. 1, 2, 3 FULLY AVAILABLE VIA LINKS. PARTS OF CHAPS. 4, 5, 6, AND 18, THE FREE FIELDS WHOLENESS CHART, AND CERTAIN OTHER MATERIAL ALSO AVAILABLE VIA THEIR RESPECTIVE LINKS.
Student Friendly Quantum Field TheoryTM
Basic Principles and Quantum ElectrodynamicsTT
Chapter 1. Bird's Eye View Intro to, background for, and simplified overview of QFT. Comparison of QFT, non-relativistic quantum mechanics, and relativistic quantum mechanics. Overview of physics and how these three quantum theories are related to each other and to classical theory.
Chapter 2. Foundations Natural units, notation, summary of classical variational mechanics, Shrödinger and Heisenberg pictures, summary of quantum theories, 2nd quantization. Appendix: Simplified intro to contravariant/covariant components.
Part I: Free Fields
Chapter 3. Scalars: Spin 0 Fields Relativistic quantum mechanics (RQM): deducing the wave equation, relativistic probability density, explanation for “funny” relativistic normalization constants, negative energies. Quantum field theory (QFT): deducing the field equation, deriving coefficient commutators, number operator form of Hamiltonian, vacuum energy, creation and destruction operators, normal ordering, 4 currents, observable operators, bosons and commutators, QFT states as harmonic oscillators, step-by-small-step derivation of the propagator.
Free Fields Wholeness Chart Overview of scalars (Chap. 3), spinors (Chap. 4) and vectors (Chap. 5.) Free fields summary of theory derivation and key relations. Ranges from 2nd quantization and field equations to observables and propagators. This is the same chart found at the end of Chap. 5.
Part II: Interacting Fields
Chapter 7. Interactions: The Underlying Theory
Chapter 8. QED: Interaction Theory Applied to Electromagnetism
Chapter 9. Higher Order Corrections
Chapter 10. The Vacuum Revisited
Chapter 11. Symmetry, Invariance, and Conservation for Interacting Fields
Part III: Renormalization: Taming Those Notorious Infinities
Chapter 12. Overview of Renormalization.
Chapter 13. Renormalization Toolkit
Chapter 14. Renormalization: Putting It All Together
Chapter 15. Regularization
Part IV: Application to Experiment
Chapter 16. Postdiction of Historical Experimental Results.
Chapter 17. Scattering.
Chap 18 revised pgs (as of July 21, 2014)
Chapter 19. Looking Backward and Looking Forward: Book Summary and What’s Next
Non Eigen States, Wave Packets, and the Hamiltonian in QFT A look at states in QFT which are not eigenstates of three momentum k, and additionally, wave packet states in QFT. The action of the QFT Hamiltonian on these states is investigated. This material does not seem to be available in any QFT texts.
Chirality and Helicity
Chirality vs Helicity summary A summary chart explaining, comparing, and contrasting chirality and helicity, two concepts that are often confused for one another.
Chirality and Helicity in Depth Closer look at chirality and helicity using examples, rather than pure theory. Also shows how chirality and helicity become effectively the same thing when v=c.
Green Functions and the Generating Functional
Green functions and the generating functional A presentation of material shown in other texts, but a done a little differently (easier to understand, hopefully) here. Among other things, it shows the connection between the Green function of usual mathematics and the Green function methodology of QFT. This document only covers the canonical quantization approach. For a comparison with the path integral approach, see the wholeness chart link below.
Wholeness Chart for Green Functs and Generating Functional in Canonical and Path Integral Approaches A two page summary of the key relationships and where they come from for Green functions and generating functionals. Compares the canonical quantization version to the path integral version and illustrates how they are effectively the same thing.
Lie groups and algebras A simplified introduction to Lie groups and algebras written by one of the book readers, Doug McKenzie (not by R. Klauber), and intended to be as easy as possible to understand.
Seesaw Mechanism A way in which the low mass of neutrinos may be explained.
Strong Force Gauge Invariance Proof A step-by-step proof of the gauge invariance of the quark color (QCD) Lagrangian under SU(3) transformation. This is often just stated by authors or left to the reader to derive.
Author’s Research Related to Zero Point Energy Cancellation
Mechanism for Vanishing Zero Point Energy (2003). See footnote on pg. 50 of text.
A fundamental, and previously unrecognized, inherent symmetry in quantum field theory appears to provide a resolution of the large vacuum energy problem, simply and directly, with no modification or extension to the extant mathematics of the theory.
Supplemental Solutions to the Field Equations: Norms, Observables, and Propagators (2005). See text footnote pg. 50.
The metric for the subspace of the “supplemental” solutions to the QFT field equations is shown to be indefinite with some states possessing negative norms. This issue is resolved, and the incorporation of such solutions into QFT found to be consistent, by appropriate definition of supplemental observable operators.
Derivation of the Supplemental Particle Propagator. Proof that the propagator for supplemental particles is the same as that of the traditional particle, but with opposite sign. Deduced in 2005 article above, but presented in pedagogic detail in this document.
Cosmic Microwave Background: A Student Friendly Intro. An introduction to the cosmic microwave background power spectrum analysis half-way between available website popularizations and a typical cosmology text. Suitable for those with an undergraduate physics background.
The Central Limit Theorem. A step-by-step, simplified explanation of the central limit theorem of statistics, with histogram examples at every step.
Copyright © 2005, 2007, 2009, 2010 to 2015 of Robert D. Klauber. Until and unless other notice is given, copies of material found herein may only be made by students, instructors, and others solely for their personal use. To include any original material, or original presentation of known material, contained herein in a publication, written prior approval from Robert D. Klauber, or his heirs, is required.