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Abstract: The unification of Quantum Mechanics and General Relativity remains theprimary goal of Theoretical Physics, with string theory appearing as the onlyplausible unifying scheme. In the present work, in a search of the conceptualfoundations of string theory, we analyze the relational logic developed by C.S. Peirce in the late nineteenth century. The Peircean logic has themathematical structure of a category with the relation $R {ij}$ among twoindividual terms $S i$ and $S j$, serving as an arrow or morphism. Weintroduce a realization of the corresponding categorical algebra ofcompositions, which naturally gives rise to the fundamental quantum laws, thusunderscoring the relational character of Quantum Mechanic. The same relationalalgebra generates a number of group structures, among them $W {\infty}$. Thegroup $W {\infty}$ is embodied and realized by the matrix models, themselvesclosely linked with string theory. It is suggested that relational logic and ingeneral category theory may provide a new paradigm, within which to developmodern physical theories.



Author: A.Nicolaidis

Source: https://arxiv.org/



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