Category Theoretic Background
Friendly introductions to this approach are found in:
- Bob Coecke, Kindergarten quantum mechanics
- Bob Coecke, Introducing categories to the practicing physicist
More related material is available from Samson Abramsky, Bob Coecke and Peter Selinger's respective homepages. Similar ideas can also be found in work by John Baez, Louis Kauffman and Robin Houston (blog).
- http://arxiv.org/abs/quant-ph/0407224
- http://arxiv.org/abs/quant-ph/0404040
- http://arxiv.org/abs/math.CT/0604542
Category-theoretic background:
- The use of graphical calculi in physics can be traced back to a 1971 paper by Roger Penrose: Applications of Negative Dimensional Tensors in Combinatorial Mathematics and its Applications, ed. D. Welsh, Academic Press, New York, 1971, pp. 221-244..
- Full and faithful categorical semantics for these kinds of calculi was provided by Joyal and Street, and Freyd and Yetter, and implicitly also already in the pioneering work by Kelly and Laplaza, in their paper Coherence for Compact Closed Categories.
- The connection between classical and quantum structures in the symmetric monoidal approach is strongly inspired by the paper of Carboni and Walters (1987), Catesian Bicategories I, Journal of Pure and Applied Algebra 49, pages 11-32, in which they introduced Frobenius comonoids.
- The first connections to logic are mainly due to Lambek, and have now become part of the vast body of research on linear logic.
