Index
angular momentum, 104
atlas
of a vector bundle, 145
automorphic factor, 181
basis
complex unitary, 28
dual, 11
L-related unitary, 29
real unitary, 28
related symplectic, 22
symplectic, 12
Bianchi identity, 161
bundle,
characteristic, 87
cotangent, 45, 147
differentiable vector, 146
tangent, 147
vector, 144
canonical form, 12
characteristic line fields, 91
Christoffel symbol, 159
coadjoint orbit, 110
coadjoint cocycle, 96
coadjoint orbit, 54
coboundary operator, 52, 172
cocycle identity, 96
cocycle relation, 145
cohomology groups
De Rham, 175
of a group, 172
of a Lie algebra, 52, 174
of a manifold, 175
configuration space, 1, 45
conjugation, 53
connection, 48, 158
integrable, 161
contact manifold, 86
weak, 85
contravariant or covariant vector, 149
coordinates, symplectic, 36
cotangent space, 142
covariant derivative, 158
curvature matrix, 161
derivation, 141, 164
diffeomorphism, 139
symplectic, 83, 84
different iable function , 139
differentiate section, 146
differential form
closed, 155
covariant derivative of a, 162
degree 1, 148
exact, 155
qth degree, 153
reduced representation, 153
skew symmetric representation, 154
differential system, 56
involutive, 57
differentiation, exterior, 154
dual space, 11
energy function, 74
equations of motion for a charged particle,
75
Euler-Lagrange equation, 2
exponent map, 168
fiber derivative, 102
flow, 41, 156
189
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