Bert Schroer has sent me some notes comparing the Lagrangian path integral and algebraic approaches to quantum field theory, which others may also find interesting. I have a very different perspective than he does, but have gone through the experience of at one time believing that basically all there is to QFT is to choose an action functional and then apply straightforward techniques to evaluate the path integrals you get. Non-perturbatively, this works beautifully for Yang-Mills theory, but runs into serious problems in many other cases, and it becomes clear that the path integral method, for all its virtues, does hide some very real problems.
Update: Some more notes from Schroer on AQFT.
Some other unrelated links:
There’s an extremely well-known story about the young Gauss, and it turns out that, as almost always with such stories, the truth of what actually happened is rather elusive. American Scientist has a wonderful article about this by Brian Hayes entitled Gauss’s Day of Reckoning.
The AMS has announced a Leonard Eisenbud Prize for Mathematics and Physics. It will be awarded every three years for a work published in the preceding six years that brings the two fields closer together. The first award will be made in January 2008. The prize was established by David Eisenbud (currently director of MSRI) and his wife in honor of Eisenbud’s father, who was a mathematical physicist.
While I was away the Museum of Natural History here in New York sponsored a debate on the Multiverse, entitled “Universe: One or Many?”. For some reports on the debate, see here, here and here. The last of these is from local blogger “mighty dasmoo”, who really, really, doesn’t like Michio Kaku.
The EPP 2010 Panel will release its final report to the public at a press conference in Washington on April 26.
Update: New Scientist also has some quotes from the “Universe: One or Many?” debate:
Kaku, of the City University of New York, spoke at one point of the possibility of tunnelling into other universes through space-time foam, harnessing the power of negative energy. “Genesis happens all the time,” he said. “Continuous genesis in an ocean of Nirvana, and the ocean is an 11-dimensional hyperspace.”
As Kaku spoke, Krauss, of Case Western Reserve University in Cleveland, Ohio, looked as if he was about to have an aneurysm. He turned to Kaku. “If there are an infinite number of universes,” he declared, “I can’t imagine one in which I agree with what you just said.”
Update: Another report on the debate is here.
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