Volumes 1 and 2


“All chapters are pedagogically brilliant”

Physics from Symmetry by J. Schwichtenberg*


“the only text I’ve come across as a student that I would categorize as a ‘must buy’”

                                                                  See review

“a pedagogic masterpiece”

                                                             See review


Book/Website Aim

The two volumes of this set and this website aim to make learning, and teaching, quantum field theory (QFT) easier, and thus, more efficient and fulfilling.

The books 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


   Vol 1 front cover, full size

          Vol. 1 back cover



Preface Vol 1

Preface Vol 2

(Prefaces summarize pedagogic principles employed)

Vol 1 Contents, Downloads

Vol 2 Contents, Downloads

Corrections to the books

Provide feedback

Auxiliary material

Advanced material

Other topics

Author's research on ZPE

Buy the Books and the Problem Solutions Booklets

See the links below to order one or more of the books.

Note Volume 1 is in the 2nd edition. Volume 2 is 1st edition. Do not confuse editions with volumes when you order. The ISBN numbers below can help in this regard.


Students: Get the Books for Free

If you get your school library to order one or more of the books, you can get free copies for yourself. See here for details.



    Volume 1 (2nd Edition)

Student Friendly Quantum Field Theory: Basic Principles and QED

If you buy the book, the latest version is highly recommended. For reasons, see Information on Both Volumes.

Buy Volume 1 here

A booklet with solutions to problems is also available. See Vol 1 problem solutions booklet.



Volume 2

Student Friendly Quantum Field Theory, Volume 2: The Standard Model

If you buy the book, the latest version is highly recommended. For reasons, see Information on Both Volumes.

The books are available on Amazon at the links below.

Hard Cover Volume 2 of SFQFT Amazon link  ISBN 978-0-9845139-7-0

Soft Cover Volume 2 of SFQFT Amazon link ISBN 978-0-9845139-8-7

Solutions to Problems for Volume 2 of SFQFT Amazon link ISBN 978-0-9845139-9-4




Outside the USA

The texts and solutions books are also being sold in many countries outside the USA through local booksellers, where residents will not have to pay international shipping rates. See www.quantumfieldtheory.info/country_list_SFQFT.htm for a list of countries, and retailers therein, where the books are available.

Contents of Volume 1



Student Friendly Quantum Field TheoryTM (Volume 1)

Basic Principles and Quantum ElectrodynamicsTT

Preface of Volume 1  (Downloadable.)

Chapter 1. Bird's Eye View  (Downloadable.)

Chapter 2. Foundations  (Downloadable.)

Part One: Free Fields

Chapter 3. Scalars: Spin 0 Fields  (First part of chapter downloadable.)

Chapter 4. Spinors: Spin 1/2 Fields 

Chapter 5. Vectors: Spin 1 Fields 

Chapter 6. Symmetry, Invariance, and Conservation for Free Fields (First part of chapter downloadable.)

Free Fields Wholeness Chart  (Downloadable.) Overview summary in chart form of free fields theory derivations and key relations for scalars (Chap. 3), spinors (Chap. 4) and vectors (Chap. 5).

Part Two: Interacting Fields

Chapter 10. The Vacuum Revisited (Downloadable.)

Part Three: Renormalization: Taming Those Notorious Infinities

Part Four: Application to Experiment


Chapter 18. Path Integrals in Quantum Theories: A Pedagogic 1st Step (First part of chapter downloadable.)


Student Friendly Quantum Field TheoryTM, Volume 2

The Standard Model

Preface of Volume 2   (Downloadable.)

Chapter 1. Bird's Eye View: The Standard Model  (Downloadable.)

Part One: Mathematical Preliminaries

Chapter 2. Group Theory  (Downloadable.) Introduction to group theory for application to the standard model. Simplified language, many examples, and wholeness charts.

Part Two: QED Revisited: Path Integrals

Part Three: Electroweak Interactions

Part Four: Strong Interactions

Part Five: Summary of the Standard Model and Beyond


Auxiliary Material (Augments Volume 1. All downloadable.)

Summary of Special Relativity. A wholeness chart of the key relations/equation in special relativity theory along with explanatory notes on how they were arrived at.

Pedagogic Aids to Chap 2 of SFQFT. Some background info to help with Chap. 2 for those who may not be well versed in certain concepts from quantum mechanics taken for granted in that chapter.

Dirac delta function forms . A summary chart of different forms for the Dirac delta function depending on whether the volume is infinite (with no boundary conditions) or finite (with boundary conditions) for both 4D spacetime and 4D momentum space.

ALL OF VOL 1 AUXILIARY FILES BELOW Click on link at left for a zip file containing all auxiliary files for Vol. 1 listed below.

Glossary of book symbols

Box2_2_comments My purpose in this box was to give a derivation of (B2-2.3) that was much simpler than that in other books. There are some subtleties involved, but it is best not to worry about them until after you have mastered QFT. If at that time, you feel up to it, check out this link.

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.

Continuous Solutions Creation and Destruction Operator Derivation A derivation and explanation of creation/destruction operators for the continuous solution form of the field equations shown in Chap. 10. Scalars only, though spinor and vector derivations are parallel.

Vacuum Fluctuations Update (Added Appendix F for Chap 10). Overview of recent experimental results on vacuum fluctuation detection, a new theoretical paper on the Casimir plate effect, and the role of the vacuum in spontaneous emission.

Symmetries Summary External vs Internal. A wholeness chart summary of symmetries comparing and contrasting internal vs external symmetries and what is conserved in each case. Probably best after digesting Chap. 6 in Vol. 1. The second page is for superstring theory and should be ignored until, and if, you study that. (Revised Jan 13, 2023).

Solution to text Prob. 17-7.

Spreadsheet for text Fig. 18-3

Alternative derivation for Sect. 18.9.2.  Thanks to Luc Longtin (not by R. Klauber).

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 QFT texts.


Auxiliary Material (Augments Volume 2. All downloadable.)

Derivation of (2-25) and Derivation of (2-28) from general principles for those who really want to get into the math. Thanks to Luc Longtin (not by R. Klauber).

Proofs of gamma matrix trace relations (5-87). Thanks to Luc Longtin.

Addendum to Appendix A of Chap. 8 An aide to understanding polarization bases for vector fields, with particular focus on massive vector fields. Helps with Appendix A of Chap. 8. Added to June 2022 revision.

Spinor Lorentz transformation . An elaboration on the Lorentz transformation of spinors, pg. 153.


Advanced  Material (Beyond, or not in, the texts. All downloadable.)

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

Freeze-out in the Early Universe Description of how particles, like possibly dark matter, “freeze-out” of the particle “soup” shortly after the Big Bang.

Group Theory

        Lie groups and algebras for NRQM spin applications A pedagogic introduction to Lie groups and algebras with applications to spin 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.)

Vacuum Fluctuations as Correlation Functions More on “vacuum fluctuations” beyond that of Chap. 10 in Volume 1. Evaluation of correlation functions as a means of measuring vacuum field fluctuations.



Other Subjects (Pedagogic presentations of topics not directly related to QFT. All downloadable. )

String theory pedagogic summaries and notes. Introductory level summaries and pedagogic notes on areas of string theory that are typically difficult to understand and/or confusing.

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.

Different Horizons in Cosmology . Wholeness charts, simplified definitions, and simplified math derivations for the Hubble sphere distance, the particle horizon, and the event horizon. First wholeness chart does not require general relativity background. The rest of the article does.

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.

Simplified Guide to de Sitter and Anti-de Sitter Spaces . Anti-de Sitter space is a key element in the famous AdS/CFT correspondence. This article explains it and de Sitter space, with almost no math, in the main part of the text at a level suitable for intelligent lay persons. The appendix deals with Einstein’s GR field equation and is technical.

Distinguishable vs Indistinguishable Particle Systems . A one-page wholeness chart summarizing, comparing, and contrasting two particle systems in NRQM where the particles are distinguishable or indistinguishable.

The Central Limit Theorem. A step-by-step, simplified explanation of the central limit theorem of statistics, with histogram examples at every step.

Generators. A wholeness chart summary of generators of translation, rotation, and boost. Points out (as shown in virtually no texts) how the classical generator uses Poisson brackets, which are replaced in quantum theory with commutators. Summarizes Sects. 11.5 and 11.6 of Zwiebach (A First Course in String Theory 2009). This link also appears below in String Theory Topics section.

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



Author’s Research Related to Zero Point Energy Cancellation and More (All downloadable.)

Mechanism for Vanishing Zero Point Energy (2003). See footnote on pg. 50 of Vol. 1.

This article has been updated, expanded, and improved in the link below.

Mechanism for Resolving Gauge Hierarchy and Large Vacuum Energy (Feb 2018, original title: A Symmetry for Resolution of Gauge Hierarchy, Null ZPE, and Null Higgs Condensate Energy). Use of alternative forms for solutions to the QFT field equations provides 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.



Sit down before fact as a little child, be prepared to give up every preconceived notion, follow humbly wherever and to whatever abysses nature leads, or you shall learn nothing.

                                                                                                                            Thomas Henry Huxley


“My grandmother had always referred to the universe as ‘The Great Mystery’.

Mystery fills us with awe and wonder. It is the foundation of humility, and humility is the foundation of all learning.”

                                                                                                                            Protagonist in the movie Indian Horse.



Copyright © 2005, 2007, 2009 to 2023 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.


  * Jakob Schwichtenberg, Physics from Symmetry (2nd ed., Springer 2018) Chap. 9, pg. 228, Further Reading Tips.

       † See two quotes from students herein plus this review.





Student Friendly Quantum Field Theory