Pedagogic Aides to

Quantum Field Theory

Statement of Web Site Purpose

The goal of this web site is to provide assistance in learning quantum field theory (QFT). It is an outgrowth of my own notes on how one could present the subject in a more student friendly manner, compiled when I was first studying QFT over 20 years ago.  In that sense, it is a sort of “peer instruction” (a teaching tool of recognized merit.)

The material herein is part of a textbook I am presently writing, in which I hope to make learning QFT markedly easier, and thus more efficient, than do typical texts.  The pedagogic principles to be employed in so doing are summarized in a preliminary preface to the text (see Preface.)

As but one example, material is often overviewed/summarized in what I call a “Wholeness Chart” (called a “Unifying Chart” in my earlier work), so named because it reveals in chart form the underlying connections that unite various aspects of a given theory into a greater whole.  Learning a computer program line-by-line is immensely harder than learning it with a block diagram of the program, showing major sections and sub-sections, and how they are all interrelated.  The same is true in physics. Wholeness Charts for physics parallel block diagrams for computer programs and, I submit, are just as advantageous for the learning process.  A picture is worth a thousand words, and in my own learning experiences, I have found Wholeness Charts to be invaluable aids that coalesce a lot of different information into one central, easy-to-see, easy-to-understand, and easy-to-reference, framework.

This web site is neither static nor comprehensive.  It is currently quite rudimentary, and should, with time, change and expand dramatically.  Rather than wait until (and if) the book were finished, I felt it advantageous to make certain core material available online as it became completed.  Hopefully, with time permitting, there will be much more to come.

Regardless of the state of evolution of the site, I hope that whatever students of QFT find here will be helpful.

                                                                                                Robert D. Klauber, PhD

                                                                                           August 1, 2009

Feedback Welcome

If you find errors herein or have suggestions on how any aspect of QFT might be presented in an easier to understand manner, please let me know via rdklauber###quantumfieldtheory.info (### used to thwart bots and spam - change ### to “at” sign.)

Contents

Major Sections:

Introduction-Background (Chapter 1 of text entitled “Bird’s Eye View”. Intro to, background for, and simplified overview of QFT.)

Latest significant revision: September 18, 2009. This link has January 27, 2010 revision incorporating a spelling correction plus 3 added words in Sect 1.5.2.

Chapter 2. Foundations (Natural units, notation, summary of classical variational mechanics, Shroedinger and Heisenberg pictures, summary of quantum theories, 2nd quantization. Appendix: Simplified intro to contravariant/covariant components)

                        Latest revision: Jan 27, 2010 has corrections on pg 34 to Oct 1, 2009 version.

Chapter 3. Scalars: Spin 0 Fields (Partially complete version includes relativistic quantum mechanics (RQM), but not yet QFT. Covers deducing the Klein-Gordon equation, solutions to it, probability density in RQM, 4 currents and conserved quantities, how negative energies arise in RQM.)

                        Original post January 31, 2010. Corrected revision February 1, 2010.)

Wholeness Chart 3-X Part 1 (Free Fields: Summary overview from field equations to propagators & observables.) Wholeness Chart 3-X Part 1 pdf version

Wholeness Chart 3-X Part 2 (Interacting Fields: Summary overview from observables/operators to Feynman rules.) Wholeness Chart 3-X Part 2 pdf version

Wholeness Chart 3-X Part 3  (Not completed at present.  Scattering and Decay summary overview.)

Wholeness Chart 3-X Part 4  (Not completed at present.  Renormalization summary overview.)

Path Integrals in Quantum Theories: A Pedagogic 1st Step  pdf vers  (Feynman’s many paths approach: the other way  besides canonical quantization  to do QFT.  Added April 30, 2009.  Modified May 6, 2009.)

Auxiliary Sections:

Probability Density in Relativistic QM and QFT  (The differences between probability density in non-relativistic quantum mechanics and relativistic quantum theories.  A confusing topic for students not explained in any text known to the author.)

Why we use "funny" normalization factors in the relativistic solutions  (This is actually the same link as probability density above.  These two topics are closely related.)

Derivation of the Propagator - Step by Baby Step (Simplified, easier to follow than almost any text.)

Compton Scattering Transition Amplitude (Step by small step derivation showing general methodology for finding any interaction transition amplitude.  This is the formal, i.e., long, method, not using Feynman rules.  Feynman rules are the shortcut derived from this method.)

Chirality and Helicity  (Added October 29, 2007)

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.)

Heisenberg Eq of Motion Yields Field Eqs (Showing how Heisenberg operator equation of motion is equivalent to the field equations of motion that QFT begins with.  This is done in Peskin and Schroeder p. 25, but one or two steps there are very obscure.  Klein-Gordon equation only.)

The Seesaw Mechanism (A way in which the low mass of neutrinos may be explained.  Advanced material.  Added on October 19, 2007.)

More to come in the future.

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Copyright

Copyright © 2005, 2007, 2009, 2010 Robert D. Klauber.  Until and unless other notice is given, free distribution of paper and electronic copies to students is permitted and encouraged, provided appropriate notification is given of this web site as the source.  Free distribution of ten or fewer copies to others is also permitted.  To include any original material, or original presentation of known material, contained herein in a publication, written prior approval from the author is required.