Index 241
number operator, 12, 16, 28, 30, 35, 104
observables
classical, 4
maximal set of compatible, 151
quantum, 4, 64
space of, 7, 9
operator, 19, 24, 25, 40
adjoint, 92
bounded, 89
closable, 94
closed, 94
closure, 94
creation/annihilation, 11, 12, 26, 29,
33, 35, 37, 38, 104
density matrix, 8
essentially selfadjoint, 97
Fourier-Plancherel, 100
Hermitean, 97
momentum, 5, 10, 15, 102
normal, 97
position, 5, 10, 15, 102
projection, 8
range of, 88
selfadjoint, 97
standard domains of composition, 88
symmetric, 97
trace of, 137
trace-class, 137
unitary, 97
orthomodularity, 135
orthonormal set of vectors, 87
Osterwalder-Schrader, 223
positivity, 224, 226
partition function, 36, 43, 46, 47, 60
path integral, 39
in coordinate space, 42
in imaginary time, 43
with coherent states, 44
Pauli matrices, 11
Peierls brackets, 220, 234–236
phase space, 4, 6, 47, 55
Poincar ́e
group, 197, 199, 200
invariance, 201, 204
symmetry, 223, 227
Poisson
bracket, 5, 24, 194, 202, 203, 205, 235,
236
tensor, 23, 62
probability, 8, 16, 30
amplitude, 144
density, 9, 17, 40
measure, 7
transition, 144
projective representation, 48, 162
quantization, 4, 6, 202, 215
canonical, 5, 15, 201
covariant, 220
geometric, 6
path integral, 39
second, 2
quantum field theory, 191, 195, 200, 208,
211, 214, 215, 221
reflection positivity, 222
relativity, 193, 197, 199
resolution of the identity, 33, 37–40, 45,
108
Riemann, 192
Riemannian
form, 20
metric, 22
tensor, 23
scalar field, 201, 208, 224
Schr ̈odinger, 2
equation, 14, 19, 167
lagrangian, 46
representation, 196, 205
Schwinger, 190
formula, 227
function, 224, 225
selfadjoint generator, 166, 171
separability, 135
spectral
condition, 200
decomposition, 4, 9, 17, 114
spectrum, 105
continuous spectrum, 105