499 research outputs found
Categorical Foundation of Quantum Mechanics and String Theory
The unification of Quantum Mechanics and General Relativity remains the
primary goal of Theoretical Physics, with string theory appearing as the only
plausible unifying scheme. In the present work, in a search of the conceptual
foundations of string theory, we analyze the relational logic developed by C.
S. Peirce in the late nineteenth century. The Peircean logic has the
mathematical structure of a category with the relation among two
individual terms and , serving as an arrow (or morphism). We
introduce a realization of the corresponding categorical algebra of
compositions, which naturally gives rise to the fundamental quantum laws, thus
indicating category theory as the foundation of Quantum Mechanics. The same
relational algebra generates a number of group structures, among them
. The group is embodied and realized by the matrix
models, themselves closely linked with string theory. It is suggested that
relational logic and in general category theory may provide a new paradigm,
within which to develop modern physical theories.Comment: To appear in International Journal of Modern Physics
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