“All chapters are pedagogically brilliant”

Physics from Symmetry by J. Schwichtenberg*


“a pedagogic masterpiece”


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

Parts of Chaps. 3, 6 & 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

Updated Revisions of Text and Solutions Booklet Now Available

New versions of both the text and the solutions booklet were published in September 2018. All errata known up to that date have been corrected, pedagogic improvements have been incorporated, and some material has been updated to reflect recent experiments and published papers.

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  (Downloadable.)

Chapter 2. Foundations  (Downloadable.)

Part I: 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 II: Interacting Fields

Chapters 7 to 11.

Part III: Renormalization: Taming Those Notorious Infinities

Chapters 12 to 15

Part IV: Application to Experiment

Chapters 16 and 17


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

Chapter 19. Book Summary and What’s Next


Auxiliary Material (Augments book. All downloadable.)

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.

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. All downloadable.)

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.

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 December 17, 2019.

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.

Group Theory

        Group Theory for QFT A draft of what will be Chapter 2 for volume 2 of Student Friendly QFT. Introduction to group theory for application to the standard model. Simplified language, many examples, wholeness charts, and solutions to problems.

        Reducible and Irreducible Groups: Direct sums, invariant subspaces, and reducibility. Not included in above chapter on group theory as it is not so relevant for the standard model. (It is relevant for more advanced theories.)

        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.)

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.



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

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.

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

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


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 text.

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.



Copyright © 2005, 2007, 2009 to 2019 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