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Created On
3 Jul 2017 14:25:34 UTC
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Physics, Topology, Logic and Computation: A Rosetta Stone
From the abstract:
"In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear
that underlying these diagrams is a powerful analogy between quantum physics and topology. Namely, a lin-
ear operator behaves very much like a ‘cobordism’: a manifold representing spacetime, going between two
manifolds representing space. This led to a burst of work on topological quantum field theory and ‘quan-
tum topology’. But this was just the beginning: similar diagrams can be used to reason about logic, where
they represent proofs, and computation, where they represent programs. With the rise of interest in quantum
cryptography and quantum computation, it became clear that there is extensive network of analogies between
physics, topology, logic and computation. In this expository paper, we make some of these analogies pre-
cise using the concept of ‘closed symmetric monoidal category’. We assume no prior knowledge of category
theory, proof theory or computer science."
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