“a pedagogic masterpiece”

                                     (See review)  



Book/Website Aim

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.”

“.. transforming the education and understanding of so many students ...”

“I have studied the subject more than once but never found the conceptual clarity you bring. I'm solving some long lived doubts and enjoying it.”

 “Your ..presentation of .. QFT is the best …I have ever seen!”

“I’m a Ph.D. student in astrophysics and cosmology. Our department [uses a different QFT text, but] I gained the best scores in [my] class .. because of your clear/elegant/magnificent book. I am sincerely grateful ... All students, like me, thank you for writing such a pedagogic masterpiece. I [will] definitely always remember what I have learned from your teaching style.”

"This book is truly fantastic."

More comments by students and physicists


Front cover, full size

Back cover



Preface (summarizes pedagogic principles employed)

Book Table of Contents


All of Chaps. 1, 2, & 3

Parts of Chaps. 4, 5, 6

Part of Chap. 18

Corrections to book

Corrections to solution booklet

Glossary of book symbols

Provide feedback


Auxiliary material

Advanced material

Other topics

Author's research on ZPE

Buy the Book and the Problem Solutions Booklet

If you buy the book, the latest version is highly recommended. For reasons, see Information on 2nd Edition.

Buy it here

A booklet with solutions to problems is also available. See problem solutions booklet.

Contents of the Book



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.

Subtleties for eq (3-47)

Chapter 4. Spinors: Spin 1/2 Fields 

Chapter 5. Vectors: Spin 1 Fields 

Chapter 6. Symmetry, Invariance, and Conservation for Free Fields

Solution to Prob. 6-14.

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.

Solution to Prob. 17-7.



Chapter 18. Path Integrals in Quantum Theories: A Pedagogic 1st Step 

Chap 18 revised pgs  (as of July 21, 2014)

Spreadsheet for Fig. 18-3.

Alternative derivation for Sect. 18.9.2

Chapter 19. Looking Backward and Looking Forward: Book Summary and What’s Next


Auxiliary Material (augments book)

Glossary of book symbols

Subtleties for eq (3-47)

Solution to text Prob. 6-14.

Spins, Spinors, and Boosts . How the change in spinor basis vector amplitudes can be determined when a general case spinor is boosted.

Vacuum Fluctuations: Recent Work. Overview of recent experimental results on vacuum fluctuation detection and a theoretical paper on the Casimir plate effect not covered in Chap. 10.

Solution to text Prob. 17-7.

Spreadsheet for text Fig. 18-3

Alternative derivation for Sect. 18.9.2

Non Eigen States, Wave Packets, and the Hamiltonian in QFT (Updated with corrections June 1, 2016.) 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


Advanced  Material (beyond the level of the text)

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.

Conformal and Scale Invariant Transformations A simplified explanation of conformal and scale invariance.

Continuous Solutions Creation and Destruction Operator Derivation A derivation and explanation of creation/destruction operators for the continuous solution form of the field equations. Scalars only, though spinor and vector derivations are parallel.

Electroweak Symmetry Breaking. The electroweak symmetry breaking model of Glashow/Salam/Weinberg is presented in a pedagogic manner by leading up to it with the simpler to understand symmetry breaking models of Goldstone and Higgs. A wholeness chart summarizing and comparing all three models is included, as well as a separate wholeness chart for each particular model. Key results are deduced via detailed step-by-step derivations, many of which are not found in texts. Updated November 22, 2017.

Green Functions and the Generating Functional

Green functions and the generating functional (Expanded and revised February 2016) 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.

Quantum Fields in General Relativity A collection of pedagogic notes on quantum fields in gravity and accelerated systems. Includes an introductory wholeness chart for scalar fields in general relativity, quantum fields in expanding universes, the Fulling-Davies-Unruh effect, and Hawking radiation. Also includes the same article whose link is below on vacuum fluctuations as correlation functions, as that is relevant for the early universe and its subsequent evolution. Based on the book by Mukhanov and Winitzki (see full citation at link.)

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.

Vacuum Fluctuations as Correlation Functions More on “vacuum fluctuations” beyond that of Chap. 10 in the text. Evaluation of correlation functions as a means of measuring vacuum field fluctuations.


Author’s Research Related to Zero Point Energy Cancellation and More

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 little modification or extension to the extant mathematics of the theory.

A Symmetry for Resolution of Gauge Hierarchy, Null ZPE, and Null Higgs Condensate Energy (Feb 2017). The symmetry of the above article is explored further and found to provide a possible resolution of the gauge hierarchy problem without SUSY, as well as a means to zero out troubling large theoretical vacuum energy densities.

Supplemental Solutions Background. Derivations of key relations used in the above two articles are presented.

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.



Other Subjects (pedagogic presentations of topics not directly related to QFT )

Brief Summary of Cosmology . A wholeness chart summarizing the most fundamental relations in cosmology, such as the Friedmann and dynamic equations, local energy conservation, critical density relation, travel time, Hubble plots, and acceleration. Comments summarize how each relation is derived.

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.

Converting Word Documents to LaTeX . A guide to using Word to write technical papers and then converting to LaTeX.



Copyright © 2005, 2007, 2009, 2010 to 2017 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.





Student Friendly Quantum Field Theory