Physics, Topology, Logic and Computation: A Rosetta Stone Export

@article{citeulike:4121553, 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.}, archivePrefix = {arXiv}, author = {{Baez}, J. C. and {Stay}, M.}, citeulike-article-id = {4121553}, citeulike-linkout-0 = {http://arxiv.org/abs/0903.0340}, citeulike-linkout-1 = {http://arxiv.org/pdf/0903.0340}, citeulike-linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2009arXiv0903.0340B}, day = {6}, eprint = {0903.0340}, journal = {ArXiv e-prints}, keywords = {category\_theory, expository\_paper, mathematics, quantum\_physics}, month = {March}, posted-at = {2009-10-22 22:13:23}, priority = {3}, title = {Physics, Topology, Logic and Computation: A Rosetta Stone}, url = {http://arxiv.org/abs/0903.0340}, year = {2009} }

TY - JOUR ID - citeulike:4121553 L3 - citeulike-article-id:4121553 N2 - 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. JF - ArXiv e-prints TI - Physics, Topology, Logic and Computation: A Rosetta Stone KW - category_theory KW - expository_paper KW - mathematics KW - quantum_physics AU - {Baez}, JC AU - {Stay}, M PY - 2009/March/06/ UR - http://arxiv.org/abs/0903.0340 ER -