Index
Key
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