Quantum cats? I assume we're not talking about Schrodinger's.... "Al Vilcius" <avilcius@webpearls.com> writes:
Plus there is of course the fantastic n-category approach of John Baez http://www.math.ucr.edu/home/baez/ but I have no idea yet of how this relates to QM (any hints?).
I got interested in n-categories precisely because I think they'll shed a lot of light on quantum gravity! Here are some papers where I try to explain why: Higher-dimensional algebra and topological quantum field theory, with James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105. (Not available electronically, since it contains lots of hand-drawn pictures.) Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189. Available as http://xxx.lanl.gov/abs/q-alg/9609018 Higher-dimensional algebra and Planck-scale physics, in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press, 2001. Available as http://xxx.lanl.gov/abs/gr-qc/9902017
From finite sets to Feynman diagrams, with James Dolan, in Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Bj\"orn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50. Available as http://arXiv.org/abs/math.QA/0004133
2-categories are also fundamental to my work on spin foam models of quantum gravity, but I have done my best to keep that fact secret, to avoid scaring the physicists: An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics, Springer-Verlag, Berlin. Available as http://xxx.lanl.gov/abs/gr-qc/9905087 Best, John Baez 17-Sep-2001 15:59:36 -0300,7087;000000000001-00000016