Thursday, January 20, 2005

Precision QED

In my class on quantum field theory I have been lecturing on renormalization of QED (Quantum Electrodynamics, which describes the interaction of photons with charged particles). As far as I know, QED is the most precisely tested theory of nature humans have ever developed. For example, using QED one can compute the magnetic moment of the electron mu to accuracy of about 1 part in 10^{-12}, using inputs such as the fine structure constant alpha, the mass of the electron, etc. The difficult part of the calculation involves quantum fluctuations of the photon as well as virtual charged particles and antiparticles.

The theoretical result is in good agreement with the experimental measurement: mu = 1.001159652187 ± 0.000000000004 in units of Bohr magnetons. The deviation from unity is due to the quantum effects I mentioned.

You can see here what is involved in a state of the art precision QED calculation: a teraflop cluster, 400,000 CPU hours to evaluate 200 10-dimensional Feynman integrals using Monte Carlo. (Don't forget the 128 bit arithmetic to maintain sufficient accuracy!)

Feynman, Schwinger and Tomonaga, the main architects of QED, are legendary figures of modern physics. For a superb intellectual history of the development of QED, see QED and the Men who Made It by S. Schweber. Schweber is a historian of science and theoretical physicist.


Anonymous said...

Yes, amazing stuff indeed! A true triumph of QFT.

I guess the comments I would like to add (I know you know more about this stuff than I do and would appreciate more insights!) are:

* It is truly amazing how the simplest possible gauge theory can explain phenomena to such great precision. No wonder particle theorists get carried away and have the hubris to think about `Theory of Everything'!

* The beauty is that this can be used to constrain physics beyond the standard model.

* The proper way to understand QFT seems to be as an effective field theory. Hence, one should be adding all terms consistent with U(1) gauge symmetry such as the dim-5 anomalous magnetic moment operator (dim 5) etc... The beauty is that the higher dimensional operators (result of unknown higher-energy physics) are suppressed by a large mass scale. So nature has been kind to us (also for making QED coupling weak). It need not have been that way.

I suppose this is a different perception than was in the 70s when only renormalizable theories were considered meaningful. Weinberg traces this evolution in thinking to the fact that constructing renomarlizable theory of gravity has been impossible (so far). So, QFTs are really an effective description (perhaps string theory is fundamental?).

On the other hand, non-renormalizable theories are unpredictive (fitting curve with arbitrary number of parameters)... (I found Weinberg's papers like 'Are nonrenormalizable theories renormalizable?' confusing: consistency does not mean predictivity, IMHO)

I feel more comfortable thinking that there is ultimately a renormalizable theory (like GUTs) from which all low-energy effective operators follow.

Thanks for pointing to the state of art in the field!


Steve Hsu said...

The change in perspective on renormalizability has coincided more or less with my career in physics. When I started college people were still obsessed with renormalizability, and the idea of effective field theories had not penetrated into the mainstream. Now it is readily appreciated that each length scale has its own appropriate degrees of freedom (e.g., hadrons at distances larger than a Fermi, quarks at shorter distances).

A non-renormalizable theory does have less predictive power than a renormalizable one. In the case of the chiral Lagrangian description of QCD there are an infinite number of operators, but their coefficients are actually secretly determined by the underlying QCD physics, which has no free parameters other than the quark masses and the strong coupling scale. Also, the higher dimension operators are less and less relevant to long-distance physics, so in the zero momentum limit you still have predictive power without actually solving QCD.

It could be the same thing with the "theory of everything": some underlying dynamics, perhaps with *no* free parameters (the dream of string theorists), but which appears to low-energy physicists as an effective theory with higher dimension operators suppressed by the Planck scale. The higher dimension operators are irrelevant for low-energy physics, but become more and more important as you approach the Planck scale. It may at first look like a mess, but in the end unify into a very predictive framework.

My problem is that I don't see any reason to expect only one mathematically consistent theory of quantum gravity. If there is more than one alternative (perhaps an infinite number), it is unlikely we will make progress without experimental data - and I don't see Planck accelerators in our future for some time..

Anonymous said...


Many many thanks for your additional comments!


Anonymous said...

"QED and the Men who Made It," checked out a copy and will have a go. I need more of an overview to understand how to read your post and subsequent comments. Hints are always welcome :)


Anonymous said...

I miss QFT class, though habituation becomes to dominate.

Anonymous said...


If you are still listening, another interesting book is "The Second Creation, by R P Crease and C Mann".

I found it to be the best book on the history of particle physics, with a decent layman's account (completely non-technical) of the subject.

It might help you appreciate better the wonders to modern quantum field theory, especially QED.

Anonymous said...

Happily, I look back. "The Second Creation." That will do nicely. When I was a child, I began with "One, Two, Three, Infinity."


Anonymous said...

"Wonders," an apt word.


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