Jost J. Geometry and Physics
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216 Index
p-form, 5
parabolic transformation, 65
parallel, 11
parallel transport, 11
parity, 83
particle, 121
classical, 97
partition function, 183, 196
path integral, 113
Pauli exclusion principle, 133
Pauli matrix, 52
perturbatively renormalizable, 130
Petersson–Weil metric, 74, 81
photon, 22, 133
Picard group, 68, 71
Planck’s constant, 181
Poincaré group, 59
Poisson bracket, 98
Polyakov action, 205
position operator, 110
positive chirality, 55
potential energy, 118
primary superfield, 200
principal bundle, 35, 36
principal fiber bundle, 48
probability, 107
probability amplitude, 112
probability distribution, 99
product bundle, 39
projection, 107
projective representation, 107
propagator, 102
propagator of free field, 183
proton decay, 134
pseudo-Majorana representation, 53
pseudo-Majorana spinor, 55
quadratic differential, 154
quantum chromodynamics, 133
quark, 134
quark confinement, 134
quasiclassical limit, 119, 120
Ramond boundary condition, 202, 203
Rarita–Schwinger field, 180
real spinor, 55
real structure, 84
reduced manifold, 87, 89
reducible representation, 128
reduction of structure group, 35
Regge slope, 182
renormalizable, 130
representation, 60
representation of Clifford algebra, 52–55, 57
Ricci curvature, 28, 47
Ricci tensor, 28, 29
Riemann normal coordinates, 24
Riemann surface, 16, 50, 64–67, 69–71, 76,
78, 92, 152, 153, 156, 157, 181, 184,
195, 202, 204
Riemann–Roch theorem, 67, 68, 74, 92, 157
Riemannian connection, 13
Riemannian metric, 18
right moving, 185
right-handed spinor, 55, 62
S-matrix, 112
Satake–Bailey compactification, 205
scalar curvature, 28, 29, 48, 195
scalar field, 135
scalar operator, 108
scaling behavior, 128
scaling dimension, 50
Schrödinger equation, 99, 111, 113
Schrödinger picture, 112
Schwarzian derivative, 197
second quantization, 100
second-order moment, 102
section of bundle, 35
sectional curvature, 28
self-dual, 6, 46
self-interaction, 135
semiclassical Einstein equations, 33
semigroup property, 111
sigma model, 151, 156, 204, 205
sign rule in super linear algebra, 83
singular terms in operator product expansion,
191
Sobolev embedding theorem, 129
space–time supersymmetry, 181
space–time symmetry, 128
space-like, 18
spin group, 51, 57, 121
spinning particle in gravitational field, 141
spinor, 63, 121, 123, 170
spinor field, 126, 127
spinor representation, 56
spinor space, 62
spontaneous symmetry breaking, 133
stable curve, 78
standard model, 132
stationary phase approximation, 182
stationary point of action, 147
strong force, 133
structure group, 35, 41, 127
sub-supermanifold, 87
super algebra, 83
super Hilbert space, 85
Index 217
super Jacobi identity, 84
super Lie algebra, 83, 89, 95, 142
super Lie group, 89
super Minkowski space, 95
super Poincaré algebra, 95
super Riemann surface, 90, 92, 179, 180, 199
super vector space, 83
super Virasoro algebra, 204
superconformal, 91, 200
superconformal algebra, 201
superconformal scaling, 180
superconformal transformation, 92, 94, 202
supercurrent, 179
superdiffeomorphism, 90, 180
superdiffeomorphism group, 179
superdiffeomorphism invariance, 179
supermanifold, 85, 86
superpoint, 87
supersphere, 92
superstring theory, 206
supersymmetric action, 159
supersymmetric interaction Lagrangian, 145,
162
supersymmetric Lagrangian, 139, 141, 145,
150, 163, 168
supersymmetric point particle, 139, 168
supersymmetric sigma model, 151, 158, 159,
161–163, 170, 178, 181
supersymmetry, 134
supersymmetry algebra, 176
supersymmetry breaking, 168
supersymmetry generator, 142
supersymmetry invariance, 150
supersymmetry operator, 166, 176
supersymmetry transformation, 160, 162, 178,
180, 201
supertorus, 93
symmetries of curvature tensor, 27
tangent bundle, 49
tangent space, 2, 49
tangent vector, 2
Taylor expansion, 85
Teichmüller direction, 73
Teichmüller space, 66
temporal ordering, 115, 189, 190
tension field, 157
tensor, 5, 49, 121
tensor calculus, 1
time direction, 18
time evolution of quantized particle, 107
time-like, 18
torsion, 10
torsion-free, 11
totally geodesic, 13
transformation, 8
transformation behavior of connection one-
form, 38
transformation behavior of curvature, 41
transformation of cotangent vectors, 4
transformation of curvature, 41, 43
transformation of metric tensor, 5
transformation of p-forms, 7
transformation of tangent vectors, 3
transition map, 34
tree level, 168
tunneling, 120, 174
two-well potential, 120
unitary transformation, 107
vacuum, 119, 135, 137
variational principles, 118
vector bundle, 35–37
vector field, 3
vector particle, 124
Virasoro algebra, 193, 199
volume form, 6, 19
Ward identity, 187, 189, 198
W boson, 133
weak force, 133
weak interaction, 134
Wess–Zumino action, 159
Weyl estimates, 184
Weyl representation, 53, 62, 63, 123
Weyl spinor, 55, 202
Weyl tensor, 29
Wick rotation, 113
Wick’s theorem, 102, 184
Wiener measure, 113
Witten operator, 166
world-sheet supersymmetry, 181
Yang–Mills connection, 44
Yang–Mills equation, 44
Yang–Mills functional, 43, 46, 48
Yau’s theorem, 206
Yukawa term, 128
Z boson, 133
zeta function, 101, 184
zeta function regularization, 184
zustandssumme, 183
zweibein, 180