Quantum Field Theory and Beyond

Abstract

It is a great pleasure and an honor to give the first talk at this symposium honoring Yukawa and Tomonaga, two giants, two pioneers of 20th century theoretical physics. I never had the pleasure of meeting them, and I look forward very much to hearing some of the stories of their lives and contributions, but I of course know very well their great contributions to elementary particle physics and to quantum field theory (QFT). Yukawa first applied QFT to the strong nuclear force, which was quite a step given that field theory had just been born a few years ago and only applied to the obvious case of electromagnetism. And he predicted the existence of the heavy meson as the carrier of the force, estimating roughly correctly its mass from the range of the nuclear force. In this sense, this was the first particle that was predicted, not on the basis of quantum theory as Einstein predicted the photon, or of symmetries as Dirac predicted the positron, but as a consequence of analysis of phenomena of elementary particle physics. It was certainly not the last particle to be predicted. Tomonaga of course developed the relativistically covariant formulation of quantum electrodynamics in parallel with Feynman and Schwinger and the theory of renormalization, thus establishing the foundations of the modern QFT. So in my talk, I am going to briefly discuss the triumph of QFT, which indeed by the end of the 20th century was triumphant as no physical theory has ever been in the past. I will also discuss the lessons that we have learned from the success of the standard model, most importantly the importance of symmetry, and the profound ways in which it appears in nature. The other important lesson we have learned goes under the name of the renormalization group or effective dynamics. Then I will briefly discuss the limitations of QFT as we turn to study the quantum dynamics of space and time, and go on to what lies beyond QFT, which I think is string theory.