Physics, Topology, Logic and Computation:
Year: 2009
Type: preprint
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’: a manifol d representing spacetime, going between two manifolds representing space. This led to a burst of work on topological quantum field theory and ‘quantum topology’. But this was just the beginning: similar diag rams 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.
Source: arXiv (Cornell University)
Authors: John C. Baez, Mike Stay
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2143735398