Wednesday, December 16, 2009

Teaching Yourself Quantum Field Theory (QFT)

QFT is nothing less than the single greatest intellectual achievement of the 20th Century if not in the entire History of  Humanity to date other than the discovery that Sex leads to Pregnancy, approximately 7000 years ago.

The two most important QFT's are Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD).

Other than enrolling in an accredited Graduate Program in Physics, there are printed resources out there that can help you understand the nuts and bolts of this great intellectual achievement.

First, master the Mathematics of Quantum Mechanics, and Special Relativity.

UPDATE: Then read the middle so-called "Hard parts" of Peter Woit's book: Not Even Wrong. In brilliant expository style, he explains (in prose form alone) how QFT came to be, beginning with the mathematics involved, notably Herman Weyl's Group Representation Theory.

Then, read “Quantum Field Theory Demystified, a Self-Teaching Book”, by David McMahon, available in bookstores and targeted to the very intelligent layperson.

UPDATE: Pursuant to Peeter Joot's first comment to this blarticle, QFT Demystified is held in rather low regard by Professional Mathematical Physicists. Peeter suggests playing a "find the Errors" game with it. Sounds like fun Peeter! I'm up to it! One can get a considerable start by reading the comments to the book at it's Amazon page. To Peeter, I agree with your comments re McMahan's QM Demystified, I never bought it.

As early as page 3 McMahon makes mention of the Klein-Gordon equation with its obvious flaws, and moves quickly into the Dirac Equation, which unified Quantum Mechanics and Special Relativity and gave birth to QFT.

On page 4 he explains that while position “x-carat” is considered an operator and time “t” a parameter in QM, and one would expect the promotion of “t” to operator status in QFT, that instead “x-carat” is considered a parameter as well, and McMahon goes on from there through its slim but lovely 261 pages.

A most popular book is "Quantum Field Theory in a Nutshell,"  by String Theorist Anthony Zee. I would not attempt this book without first mastering Mahon's work. I also own “Nutshell” as Zee refers to his book, and find it as others do a book than likely began in intent as a non-technical popular overview of QFT, then morphed somewhere along the way into a “near”-textbook without quite achieving true textbook status. Nevertheless Zee's humor is infectious, and I enjoyed it, but it is not as important as the following:

For a more Mathematical and better treatment as a textbook, Peter Woit recommends textbooks by Pierre Ramond, Peskin-Schroeder, and V.P. Nair. D.R. Lunsford recommends Michele Magiore and "Advanced QM" by Schwabi.

A wonderful discussion on QFT texts based on Zee's announcement that "Nutshell" will be re-released in 2010 with a new introduction can be found at Peter Woit's blog "Not Even Wrong" here

UPDATE (Dec. 25, 2009): I typed in  "Quantum Field Theory" at Amazon and the following books came up in the following order. I would appreciate a Professional commenting on the better ones (in addition to those already mentioned), with thanks in advance.

They are (as of today):

Quantum Field Theory by Mark Srednicki (Hardcover - Feb 5, 2007)

Quantum Field Theory in a Nutshell by A. Zee (Hardcover - Mar 10, 2003)

Quantum Field Theory Demystified by David McMahon (Paperback - Feb 29, 2008)

Quantum Field Theory by Claude Itzykson and Jean-Bernard Zuber (Paperback - Feb 24, 2006)

An Introduction To Quantum Field Theory (Frontiers in Physics) by Michael E. Peskin and Dan V. Schroeder (Hardcover - Oct 1, 1995)

Quantum Field Theory by Lewis H. Ryder (Paperback - Jun 13, 1996)

The Quantum Theory of Fields, Volume 1: Foundations by Steven Weinberg (Paperback - May 9, 2005)

A Modern Introduction to Quantum Field Theory (Oxford Master Series in Statistical, Computational, and Theoretical Physics) by Michele Maggiore (Paperback - Feb 10, 2005)

Modern Quantum Field Theory: A Concise Introduction by Tom Banks (Hardcover - Oct 27, 2008)


Peeter Joot said...

I'm suprised to see a recommendation for QFT Demystified. His book on regular QM was a mess, and not one that I would consider of much value without several other better ones to supplement it (if you have those, and are willing to play the find the typos game then his book can be worthwhile).

Steven Colyer said...

Peeter, thanks for posting. I agree with what you said and look forward to further discussion following the busy holidays.

However and as far as I know, it's the only mathematically-detailed QFT book dedicated on the subject available at major bookstore chains. Refer to the blarticle responses at Woit's blarticle I linked for more detail. I will eventually include them here following the imminent busy holidays with due credit including yours.

Renormalization: the toilet may be dirty but damned if it doesn't flush so well! Is Chris Oakley the only one trying to clean it up?

Steven Colyer said...

I just discovered a wonderful text, it's free and online (and after I spent money for Weinberg's "The Theory of Fields, Volume 1" !

The textbook is Fields, by Warren Siegel, and can be found by clicking here.

Peeter Joot said...

ps. Did you know that Srednicki has a pre-release version of the pdf for his book available:

I don't think any errata updates make it into that, but you can at least read that version and get an idea if you want to purchase the text (I don't personally know enough to try to read it yet).

Steven Colyer said...

No I did not know so I thank you very much for that, Peeter. Currently my investigations into QFT (hopefully leading to QCD which interests me most as so much work remains to done there) are being put on hold as I investigate Verlinde's "controversial" work and read Carroll's new book as well.

Entropy is a subject we Mechanical Engineers are quite familiar with, and hopefully I can contribute to the discussion down the road.