
Physics, Topology, Logic and Computation: A Rosetta Stone - danharaj
http://arxiv.org/abs/0903.0340
======
danharaj
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 linear
operator behaves very much like a "cobordism". 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 precise using the concept of "closed
symmetric monoidal category". We assume no prior knowledge of category theory,
proof theory or computer science.

