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