From Yukawa to M-Theory

Let me first refer to the historical background of my talk. I got the degree of doctor (thesis: “Composite Model of Hadrons”) under Professor S. Sakata at Nagoya University in 1956, and moved to Kyoto University at the end of 1957 after passing nearly two years at Rikkyo University, where I could come into contact with Professor M. Taketani. Professor Yukawa(1907-81) in Kyoto was just 50 aged at that time. He was in the middle of research of nonlocal field theory. I remember that he was highly sensitive to the new proposal of Heisenberg’s nonliner spinor theory(1953), which was regarded as a work aiming at “a unified theory of universe”. Surely, every things seemed exciting to us. Let me cite several important works in those days: Heisenberg: S-Matrix (fundamental length l0) (1943) Yukawa: Nonlocal Field Theory (1947 ) Snyder, Yang: Quantized Space-time (1947) Tomonaga, Schwinger, et al.: Renormalization Theory (1948) Fermi-Yang: Composite Model of π-meson (1949) Pauli-Villars: Regularization (1950) Heisenberg: Nonlinear Spinor Theory (1953) Nakano-Nishijima, Gell-Mann: Strange Particles (1953) Yang-Mills: Nonabelian Gauge Theory (1954) Sakata: Composite Model of Hadrons (1956)