

Volumes 1 and 2
“All chapters are pedagogically brilliant” Physics from Symmetry by J. Schwichtenberg*
“a pedagogic masterpiece”^{ }^{†}Book/Website AimThe 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 stepbysmallstep 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." 
(Prefaces summarize pedagogic principles employed) 

Buy the Books and the Problem Solutions BookletsSee the links below to order one or more of the books. Note Volume 1 is in the 2^{nd} edition. Volume 2 is 1^{st} edition. Do not confuse editions with volumes when you order. The ISBN numbers below can help in this regard.
Students: Get the Books for FreeIf 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 (2^{nd} 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 Volume 1. 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 The books are available on Amazon at the links below. Hard Cover Volume 2 of SFQFT Amazon link ISBN 9780984513970 Soft Cover Volume 2 of SFQFT Amazon link ISBN 9780984513987 Solutions to Problems for Volume 2 of SFQFT Amazon link ISBN 9780984513994
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 1CHAPS. 1 AND 2 FULLY AVAILABLE VIA LINKS. PARTS OF CHAPS. 3, 6 AND 18, THE FREE FIELDS WHOLENESS CHART, AND CERTAIN OTHER MATERIAL ALSO AVAILABLE VIA THEIR RESPECTIVE LINKS.
Student Friendly Quantum Field Theory^{TM} (Volume 1) Basic Principles and Quantum Electrodynamics^{TT}^{} 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 Part Three: Renormalization: Taming Those Notorious Infinities Part Four: Application to Experiment Addenda Chapter 18. Path Integrals in Quantum Theories: A Pedagogic 1st Step (First part of chapter downloadable.)
Student Friendly Quantum Field Theory^{TM}, 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.)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. Box2_2_comments My purpose in this box was to give a derivation of (B22.3) 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. 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). Spreadsheet for text Fig. 183 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 (225) and Derivation of (228) 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 (587). 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. Freezeout in the Early Universe Description of how particles, like possibly dark matter, “freezeout” 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 FullingDaviesUnruh 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. )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 halfway between available website popularizations and a typical cosmology text. Suitable for those with an undergraduate physics background. Simplified Guide to de Sitter and Antide Sitter Spaces . Antide 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 onepage 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 stepbystep, 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.
String Theory Topics: Introductory Level Energy in a Superstring. The way tension energy in a string is calculated in superstring theory differs from that of classical mechanics and so, can be confusing. (It was very confusing to me.) I have not seen any author address this issue, as the texts seem to simply slide over it. This link explains the differences in the two approaches, as well as discussing vibrational mode energy and Tduality. Gravity and Electrodynamics in Higher Dimensions. A wholeness chart comparing and contrasting the way gravity and electromagnetism are treated in higher dimensions. Units here can be very confusing as how they are handled differs in the two cases. Summary of Gauges in String Theory. A wholeness chart overview of the different gauges used to develop string theory. Symmetry on the String Worldsheet. A wholeness chart summary of symmetries comparing and contrasting internal vs external symmetries and what is conserved in each case. This is the same as the “Symmetries Summary …” above for Vol. 1 auxiliary material, but the second page is for superstring theory, so it is also included here. Point Particle vs String Solutions. A wholeness chart summary and comparison of point particle vs open string motion in the lightcone gauge. Includes equations of motion. list of independent variables, list of dependent variables, solutions to the equations of motion, and more. Augments and summarizes much of Chaps. 9, 11, and 12 of Zwiebach (A First Course in String Theory 2009). 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. This link also appears above in Other Subjects section. Deducing D=26 and M^2 Relations. An overview of how the bosonic string can only exist in 26 dimensional spacetime in order to satisfy Lorentz invariance plus insight into the M ^{2} relationship for quantized strings. Open vs Closed Relativistic String Solutions. A onepage wholeness chart listing the key parts of the solutions for relativistic strings. It compares and contrasts the solutions and underlying relations for open vs closed strings. Summary of Lagrangians for Different Systems. A wholeness chart summary of different Lagrangians used for different areas of physics. Includes and compares nonrelativistic vs relativistic and free vs interacting cases for particles, harmonic oscillators, fields (scalar, spinor, vector), and strings. Number Operators in QFT and String Theory. The number operator in string theory is similar in some respects to, and different in other respects from, that of QFT. This link is a one page wholeness chart comparing and contrasting them. Summary of Zwiebach Chapter 14 plus a simplification. An overview of Chap 14 in Zwiebach just a little over one page. The link includes two figures not shown in that text that should make the meaning of the result clearer. Also includes a simplified, half page derivation of the last relation in Section 14.3 (pgs. 309312), which takes 4 pages there.
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. CopyrightCopyright © 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 (2^{nd} ed., Springer 2018) Chap. 9, pg. 228, Further Reading Tips. † See two quotes from students herein plus this review.
