What is quantum field theory, and what did we think it was? Comments by Laurie M. Brown and Fritz Rohrlich (Q2724962)

This conference sessions transcript consists of the talk given by Steven Weinberg in which he develops on his tentative definition of quantum field theory (QFT), the historical comments by Laurie M.\ Brown and the remarks from the viewpoint of a philosopher of science by Fritz Rohrlich. Notes from the ensuing discussion are included. Summarizing, Weinberg's main point, which he himself calls a `folk theorem,' is that QFT is that one theory which satisfies Lorentz invariance, obeys the rules of quantum mechanics, and has the cluster decomposition property, saying that distant experiments yield uncorrelated results [see \textit{S. Weinberg}, The quantum theory of fields. Vol. 1: Foundations. Corr. repr. of the 1995 orig. (English) Cambridge: Cambridge University Press (1996; Zbl 0959.81002)]. As he points out, there are various caveats to consider when proposing such a broad statement, and in fact string theory, not being a field theory in the strict, Lagrangian, sense, already provides a counter example. Weinberg clarifies that one should consider QFT as a low energy effective theory of some more fundamental structure -- may it be string theory or anything else -- and that such an effective theory satisfying the above requirements will look very much like QFT. Considering Einstein and Yang-Mills theories as effective theories, one obtains a modern notion of renormalizability as opposed to that stemming from power counting: The symmetries governing the action should govern the infinities in order to allow for their step by step cancellation. Weinberg reflects on the historical failure of the stron \(S\)-matrix programme and the irony of the fact that modern effective field theory has a very similar approach in always considering the most general ansatz (\(S\)-matrix resp.\ Lagrangian) compatible with the fundamental principles, and he gives another answer to the question posed in the talks title: QFT is `\(S\)-matrix theory, made practical.' In defense of the effective field theory approach against accusations of being intellectually uninspiring, he concludes that we are `simply \dots realizing that we perhaps didn't know as much as we thought we did, \dots and now we are going to go on to the next step and try to find an ultraviolet fixed point, or (much more likely) find entirely new physics' such as string theory. In her historical comments, Laurie M.\ Brown dwells to a large extent on the issue of complementarity of wave- vs.\ particle-like nature of the basic objects of quantum theory, and how it came to a settlement of this problem in the 1920s and 30s with the realization that they lead to the same physical predictions. This was noted in the bosonic case by Dirac in 1927, and for fermions (where it appears as the contradistinction of hole theory and particle theory for electrons in quantum electrodynamics) by Furry and Oppenheimer in 1934. After a diversion on the historical development of the rôle of the \(S\)-matrix, she points out that QFT has shown that the evolution of modern science is neither pure reductionism nor unification of everything, but rather a kind of oscillation between these complementary features in a progress of exploration of the unknown. Fritz Rohrlich marks some serious pitfalls in the view of modern physics as a reductionistic venture: Many more fundamental physical theories do not reduce to their less fundamental antecendents by taking some mathematically well defined limit. This is true for exmple in the case of geometrical optics, which can be obtained from Maxwellian electrodynamics only by a singular expansion, and yet more dramatically in the case of QED, where one is not able to derive the Lorentz-Dirac equation of motion for the electron from its principles. In his words: `the more fundamental theory is not analytic at \(p=0\), where \(p\) is the small parameter that characterizes the approximation to a less fundamental theory.' Yet more fatal to theory reduction is the existence, or emergence, of incommensurable concepts in less and more fundamental theories respectively. This latter point is strongly disputed by Steven Weinberg in the session discussion, stating that while there might exist incommensurable concepts at different levels of insight, this does not prevent that those at deeper levels are effectively used to explain those at the higher ones.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00052].