From Finite Sets to Feynman Diagrams

Details From Finite Sets to Feynman Diagrams From Finite Sets to Feynman Diagrams

2000-04-20

arxiv.org/abs/math/0004133v1

In Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Bj\"orn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-

Mathematics

Quantum Algebra

30 pages LaTeX, 5 encapsulated Postscript figures

Scientific paper

`Categorification' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category of finite sets serves as a categorified version of the set of natural numbers, with disjoint union and Cartesian product playing the role of addition and multiplication. We sketch how categorifying the integers leads naturally to the infinite loop space Omega^infinity S^infinity, and how categorifying the positive rationals leads naturally to a notion of the `homotopy cardinality' of a tame space. Then we show how categorifying formal power series leads to Joyal's `especes des structures', or `structure types'. We also describe a useful generalization of structure types called `stuff types'. There is an inner product of stuff types that makes the category of stuff types into a categorified version of the Hilbert space of the quantized harmonic oscillator. We conclude by sketching how this idea gives a nice explanation of the combinatorics of Feynman diagrams.

Affiliated with

Also associated with

No associations

Rating

From Finite Sets to Feynman Diagrams does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with From Finite Sets to Feynman Diagrams, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From Finite Sets to Feynman Diagrams will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-144367