I continue to believe that “quantum field theory” is a concept that we physicists don’t do nearly enough to explain to a wider audience. And I’m not going to do it here! But I will link to other people thinking about how to think about quantum field theory.
Over on the Google+, I linked to an informal essay by John Norton, in which he recounts the activities of a workshop on QFT at the Center for the Philosophy of Science at the University of Pittsburgh last October. In Norton’s telling, the important conceptual divide was between those who want to study “axiomatic” QFT on the one hand, and those who want to study “heuristic” QFT on the other. Axiomatic QFT is an attempt to make everything absolutely perfectly mathematically rigorous. It is severely handicapped by the fact that it is nearly impossible to get results in QFT that are both interesting and rigorous. Heuristic QFT, on the other hand, is what the vast majority of working field theorists actually do — putting aside delicate questions of whether series converge and integrals are well defined, and instead leaping forward and attempting to match predictions to the data. Philosophers like things to be well-defined, so it’s not surprising that many of them are sympathetic to the axiomatic QFT program, tangible results be damned.
The question of whether or not the interesting parts of QFT can be made rigorous is a good one, but not one that keeps many physicists awake at night. All of the difficulty in making QFT rigorous can be traced to what happens at very short distances and very high energies. And that’s certainly important to understand. But the great insight of Ken Wilson and the effective field theory approach is that, as far as particle physics is concerned, it just doesn’t matter. Many different things can happen at high energies, and we can still get the same low-energy physics at the end of the day. So putting great intellectual effort into “doing things right” at high energies might be misplaced, at least until we actually have some data about what is going on there.
Something like that attitude is defended here by our former guest blogger David Wallace. (Hat tip to Cliff Harvey on G+.) Not the best video quality, but here is David trying to convince his philosophy colleagues to concentrate on “Lagrangian QFT,” which is essentially what Norton called “heuristic QFT,” rather than axiomatic QFT. His reasoning very much follows the Wilsonian effective field theory approach.
The concluding quote says it all:
LQFT is the most successful, precise scientific theory in human history. Insofar as philosophy of physics is about drawing conclusions about the world from our best physical theories, LQFT is the place to look.