What is QFT?
In 1997 Steven Weinberg published a fascinating little article What is Quantum Field Theory, and What Did We Think It Is? On 17 pages he managed to give three totally different definitions of Quantum Field Theory ...and I quote:
- "The bottomline is that quantum mechanics plus Lorentz invariance plus cluster decomposition implies quantum field theory." This suggests to me that QFT is just a mathematical formalism that allows one to satisfy these three respectable principle. It is not prohibited to look for other formalisms that satisfy the same principles. Weinberg himself says that there is no proof that QFT is the only option.
- "In its mature form the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields." Probably I was wrong, and there is no way around fields. Fields rule!
- "The present educated view of the standard model, and of general relativity, is again that these are leading terms in effective field theories." Translation: quantum field theory is not fundamental. QFT is simply a low-energy approximation to some truly fundamental theory. Needless to say that nobody has a clue what this truly fundamental theory is.
Which of these three statements is (more) correct? "Bottomline", "mature form", or"educated view"? I'll tell you my opinion in another post.