From Spacetime to Fields and Back: Elementary Domains and Their Philosophical Roots

In Tetsugaku Companion to Modern Physics and Kyoto School Philosophy. Cham: Springer Nature Switzerland. pp. 229-247 (2026)
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Abstract

In his Field Theory of Elementary Domains and Particles (1968, co-authored with Katayama Yasuhisa), Yukawa Hideki presents his programme for reconstructing particle physics based on the concept of elementary domains. Rooted in the ongoing debates surrounding relativity and quantum physics, his project pursues a twofold objective: to study particle interactions while circumventing the divergence problem of quantum field theory and to provide a unified framework for the recently discovered particle theories. This approach ultimately results in a question about the nature of spacetime. Yukawa’s answer is an audacious assumption about spacetime continuity: An elementary domain is a minimal region of spacetime with peculiar geometrical properties. In this contribution, I argue that Yukawa’s approach exemplifies a specific account of unification in physics, based on formal derivation and spatial intuition. The quantum nature of these domains reduces the entire particle content to geometrical properties, transforming the physical vacuum into a state of spacetime itself. As such, Yukawa faces the problem of illustrating how non-geometrical properties can emerge from underlying spacetime structures. I discuss how the philosophy of Nishida Kitarō might have provided the theoretical and philosophical background for the development of Yukawa’s physical theory. Ultimately, Yukawa’s attempt shows how the reconstruction of a unified particle picture presents a genuine challenge to both Eastern and Western Philosophy of Physics.

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Rossella Lupacchini
University of Bologna

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