Quantization and Categorification: Index

Mike Stay

This is an index, prepared by Mike Stay, of the notes of the Fall 2003 and Winter 2004 sessions of the Quantum Gravity Seminar. Both these sessions were part of a course on Quantization and Categorification taught by John Baez.

The index may later be expanded to cover the Spring 2004 session.


f: fall 2003 w: winter 2004 page week ----- ---- 1-11 1 12-21 2 22-26 3 27-37 4 38-46 5 47-59 6 60-69 7 70-80 8 81-91 9 92-106 10 hw: homework for winter quarter
Abel summation hw5 action group w54, w73 algebra Boolean f14, f17 commutative f1, f12, f25, w20 Heisenberg f13 Lie f11, f12 noncommutative f1, f13 Poisson f12, f25, f30 polynomial w21 R- w24 symmetric w20, w22 tensor w20 Weyl f29-30, f32, f42, f45 Bargmann-Segal f45 Fock rep f45, f67, f88, hw4 Heisenberg rep f45, f60 Schroedinger rep f32, f61 ball in a box, source of quantum weirdness f39, f96-98 Bernoulli numbers hw6-7 BLT lemma, f56 Borel measure, regular w43 boundary conditions periodic f3 calculus Fundamental theorem hw6 cardinality f6, w1, hw5, w47, w53 Catalan numbers f72-81 categorification f1, f5 creation and annihilation f89-91, w2, w12-13 differentiation f88, f92, w62 harmonic oscillator f69, w12, w38 see also harmonic oscillator hyperbolic trigonometry w63-66, hw7 natural numbers f7 power series f88, w3, w12 rig f22 see also decategorification category definition f5 coloring f69-70, hw4, w60, w67, w84-85 see also pointing coherence law w76-78 combinatorics f23 CommAlg w20 composite f5 conjugate canonically conjugate f1, f2, f30-31, w14, hw4 complex conjugate: see operator, creation and annihilation; and coordinate, in phase space conservation of energy f9 constant Boltzmann, k, w40 Planck, h or hbar, f1-2, f26-27, f50, w26 convergence radius of w8 coordinate functions f2 in phase space as complex number classical f10, f64, w22, w34 quantum f35, f42, f45, f64, f68, w34 Cubes w67 decategorification f6-7, f22 derangement hw2 derivation f12, f38 diagram, commuting: see transformation, natural Dirac delta function w44 disjoint: see union, disjoint distributive law: see functor, free divergent series creation of the devil hw5 energy f1 Euler proof that distinct and odd partitions are isomorphic hw3 sum of the natural numbers is -1/12 hw5 solution to Basel problem hw7 theorem on homogeneous functions w15 expected value f46-47, f60-61, hw4, w42-43 factorial w68 Fibonacci w6 see also Tribonacci Fermat's last theorem f19 Feynman diagrams w2-3, w51 field scalar f4 FinSet (the category of finite sets and functions) f5-7, f44 groupoid f82, w62 set of isomorphism class of objects in f6 rig f22 Fock space w13, w38 "pre-Fock space": see algebra, symmetric representation: see algebra, Weyl, Fock rep form quadratic f9 Fourier transform f2, f33, f45, f52, f62-63, f67-68 freedom, degrees of f3 functor f5, f82-83 free w21, w23 forgetful w104 see also structure types Gaussian f3, f54 generating function f69, w1, w12, w38-42, w47 ordinary vs. exponential hw3 see also partition function golden ratio w7-8 groupoid cardinality, i.e. as "fractional set" w53 zero subscript 82 growth of generating function w11; see also Hadamard's theorem Hadamard's theorem w7 souped-up w8-9, hw1 harmonic oscillator classical f8-11, f35, f37 quantum f2-3, f13, f25, f27-30, f35, f50-51, f62, f65 many degrees of freedom w12, w19, w27-37 Hausdorff space w43 Heisenberg representation: see algebra, Weyl, Heisenberg representation see also mechanics, matrix see also uncertainty principle Hermite polynomial f3, f33, f40 Hilbert space f4, w13 hotel trick f58 identity morphism f5 Jacobi f11-12, f27 inclusion-exclusion principle hw2 infinite -bonacci numbers hw1 loop: see loop, infinite matrix f2 string w27 degrees of freedom f3-4 initial weakly w78 isomorphism class f6 Jacobi identity: see identity, Jacobi Joyal, Andre f23 see also species Klein-Gordon equation f4 Lie algebra: see algebra, Lie logarithm w99 loop infinite: see infinite loop magma definition f72 matrix adjacency f15-16 infinite f2 mechanics: see mechanics, matrix stochastic f18 becomes a function over naturals f19 unitary f20 measure Borel w43 Dirac w44 mechanics Hamiltonian f8-11, f25-26, f44, f51, f60, f67, w16, w44 Lagrangian f21, f22 matrix f2, f17-f28, f31 monoid definition f13 morphism definition f5 natural numbers isomorphism class of FinSet f6 see also Euler Newton commutative p,q f96 F=ma in QM f30 object definition f5 observable classical f1, f11-12, f25-26, w42 quantum f13, f27-f30, f45, f47, f60, w42 operator bounded f31, f33, w43 creation and annihilation f35, f54, f67, w12-14, hw4-6 difference hw6 ladder: see operator, creation and annihilation lowering: see operator, creation and annihilation number f44 parity f63 projection w44 raising: see operator, creation and annihilation trace-class w43 unbounded f32 orbit of group action w54 parity see operator, parity particle classical, motion minimizes action f21 on a line f2, f25 spin-0 f4 types w2, w26 see also harmonic oscillator, quantum, many degrees of freedom partition function hw3, w36-42, w47-50 permutation w52 phase space: see coordinate in phase space Planck's constant: see constant, Planck pointing hw5 see also coloring Poisson bracket f11-12 see also algebra, Poisson probability w41 relative w40 process composition f17 definition f16 superposition f17 see also categorification, quantization, relation product Cartesian f7, f71 semidirect w83 see also quotient, weak tensor w45 property types w104 quantization f1, f3, f4, f8 quantum field theory f3, w2 quotient w52 map w74 weak w55, w75 examples w83 recoloring f86-87 recurrence hw1, w12 relation composition f15 definition f15 total f19 Riemann: see zeta function rig * f20 2 f22, w45-49 categorified f22, w24 cost f21 definition f13 free f22-23 initial f22 interference, destructive, lack of f17 examples f14-18 terminal f17 Schroedinger representation: see algebra, Weyl, Schroedinger rep see also state and wavefunction Schwartz functions introduced f32 Set (the category of all sets with functions) f82, w20 Simplices w67 singularity w11 species f23, f69 category of f87; see also structure type stabilizer w55 standard deviation f47-48 state f20, f45-47, w42 coherent f50-51, hw4 Gibbs w44 Heisenberg picture f60 mixed w43 pure w44 Schroedinger picture f61 sum over: see partition function string violin f3, w26-33 quantized w34-37 structure type composition w93 definition f82, f84 entire hw6 evaluating at a groupoid w53-62, w71-73, w86-87, w92 examples w87-98 even and odd w63 informal introduction with examples f69-71 1, being a 0-element set f71 1/(1-z), being a totally-ordered set w18 1/(1-z^2), bing a totally-ordered even set w18 1/(1-z-z^2), being a Fibonacci-structured set w4-7 (1-sqrt(1-4z))/2, being a binary tree f80-81 a,a*, creation and annihilation f89-91, f93 cosh and sinh w63 d/dz, differentiation f88, f92-93, hw2 e^z, being a finite set f92-93, w61 e^kz, being a k-colored finite set f71 k^x, being a k-coloring f85 log, being a connected graph z, being the 1-element set f76, f83-84, f89 z^n, being a totally-ordered n-element set f91 z^n/n!, being the n-element set f77, w89 rational w11 tame w60 stuff operators w106 types w51, w93, w99, w103-106 subfactorial hw2 temperature w40 dependent cardinality w48 dimension w49 thermodynamics table of comparisons w42-45 time evolution f60-68, w31, w33-35 transformation natural f5, f84 tree binary f72-75, f79, f98-99 Tribonacci hw1 uncertainty principle f35, f45, hw4 proof f48 see also conjugate, canonical underline denotes the set of isomorphism classes of objects in a category, f6 union disjoint f7, f71 unique weakly w79 universal weakly w78 vacuum w34 variance hw4 Vect w20 vector normalized f18, hw4 wave equation f3, f4, w27 wave function f20, f32 zero as subscript, indicates the underlying groupoid of a category, f82 zeta function hw5, hw7 Zustandsumme: see partition function

© 2004 Mike Stay