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| Mercier A. — Analytical and canonical formalism in physics |
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| Предметный указатель |
Gradient operator 72
Gravitation 38
Gravitation potential 38 39
Group 56
Group of Lorentz transformations 56 61
Hamilton 12
Hamilton Jacobi-equation 165 172ff
Hamilton, conservative, Jacobi-equation 3 65 173
Hamilton, non-conservative, Jacobi-equation 165 172
Hamiltonian 1 8 97 99 100 102 103 114 117 124 125 126 128 146 166ff 193 199 203ff
Hamiltonian density 144 147ff 162
Hamiltonian functional 144 146
Hamiltonian of the field (field) 126
Hamiltonian of total radiation 143
Hamiltonian, field, density 147
Hamiltonian, general, density 144 151 153 154ff
Hamiltonian, homogeneous 185 186
Hamiltonian, inhomogeneous 181
Hamiltonian, non-relativistic 182
Hamiltonian, ordinary, density 144 154ff
Hamiltonian, oscillator 141
Hamiltonian, partial 143
Hamiltonian, particular 126 128 129 130
Hamiltonian, proper 128 182
Hamiltonian, relativistic 126 130
Hamiltonian, strong 199 204ff
Hamiltonian, weak 199 204ff
Hamilton’s function (Hamiltonian) 8 99 103
Hamilton’s principle 9 11 12 13 14 16 19 33 42 52 73 74 75 109
Harmonic equation 134
Harmonic function 135
Heisenberg 6 143
Hodograph 7 105
Homogeneity 8
Homogeneous canonical formalism 131ff 172 207ff
Homogeneous Canonical transformation 165
Homogeneous configuration space 185
Homogeneous formalism 165 172 177 178ff 200
Homogeneous function 184
Homogeneous Hamiltonian 185 186
Homogeneous Lagrangian 200
Homogeneous variation principle 184 190
Homogenization 131
Homogenized configuration- & momentum-space 132
Hydrodynamics 5
Hyper cylinder 59 78
Hyper parallelepiped 85 118
Hyper sphere 116
Hyper surface 117
Hyper volume 57 58 85
Hyper, H, surface 94 114 115
Incompressibility 113
Incompressible-fluid-picture 112
Induction, magnetic-field 31 87 88 124
Induction, philosophical 78
Inertia 6 8 15 46
Inertia parameter 42 44
Inertia, moment of 16 45
Infinitesimal canonical transformation 166 197
Infinitesimal modification 196 197
infinity 118
Influence constant 88
Influence, magnetic, constant 88
Inhomogeneous canonical transformation 165 192
Inhomogeneous formalism 172 177
Inhomogeneous Hamiltonian 181
integral 118
Integral invariant 112 113
Integral, energy 2 20 49 97 121
Integral, first 17 18 20 49 97 118 119 120 121 129
Integral, momenta 9 17 19 21
Interaction 1 7 8
interval 60 61
Interval, time 62 57
Invariance 9 27 34 52 56 57 58 60 89
Invariance, canonical 165 194
Invariance, gauge 52 89 95 96
Invariance, Lorentz 126
Invariant 34 62 55 60 61 68 86 87
Invariant from epinors 66
Invariant Lagrangian density 52 93
Invariant of canonical transformation 171
Invariant of the motion 112 198
Invariant, integral 112 113
Invariant, Lorentz 60
Invariant, relativistic 127
Inverse 56
Inverse transformation 166
Isotropic line 62
Isotropic vector 61 63 64 66
Jacobian determinant 199 200ff
Juvet 72
Kepler 3
Kinetic density term 68 69 70
kinetic energy 15 16 18 22 23 27 28 39 40 41 50 68 201
Klein — Gordon-equation 160
Kronecker symbol 140
Lagrange 5 9 13
Lagrange (or Lagrangian) equation 9 12 14 16 17 19 20 21 24 27 28 31 32 34 41 42 46 48 52 83 109 110 128 205
Lagrange equation for densities 73
Lagrange formalism 97 124
Lagrange function see “Lagrangian”
Lagrangian 1 7ff 9 10 11 23 27 30 32 34 41 42 43 48 49 50 52 58 68 74 115
Lagrangian density 52 58 59 68 69 70 76 77 81 82 90 91 93 94 95 144 145 148 161
Lagrangian equation see “Lagrange equation”
Lagrangian form of electrodynamics 126 128
Lagrangian functional 60 153
Lagrangian, coordinate 76
Lagrangian, field 52 74 76
Lagrangian, homogeneous 200
Lagrangian, invariant, density 52 68
Lagrangian, preservative, density 93
Lagrangian, proper 128
Lagrangian, separable 9 48
Light 53
Light cone 37
Light, velocity of 31 38 47 53 54 124
Liouville 49
Liouville’s theorem 97 110 113 165 192ff
Liouville’s, general, theorem 165 197
Lorentz 43 47 52 53 89
Lorentz condition 89 91 133
Lorentz force 47 88
Lorentz invariance 126
Lorentz transformation 53 55 56 57 81 127
Lorentz, Maxwell, theory 87
Lorentz, Newton, equation 128
Manifold 55 61 67 85 113
Manifold, Euclidean 37 64 55 66 69 85 87
Manifold, Euclidean complex 61
Manifold, pseudo-Euclidean 54
Manifold, Riemannian 9 33 37 54 70
Manifold, sub 60
Manifold, tensorial 61
Mass 6 15 18 27 28 29 38 42 44 45 46 47 64
Mass, point 16 22
Matrix 64
Matrix, associated Cartan 64 65 66 67 72
Matrix, square 64
Matrix, transposed 66
Matrix, unit 65
Maxwell 52 90
Maxwell — Lorentz theory 87
Maxwellian 88 89
Maxwell’s equations 89 90 126 127
Maxwell’s stress-tensor 85 92
Maxwell’s theory 88
Measure in  -space 193
Mechanics (Newtonian) 38
Mercier 6 88 89 174 188 210
| Metric 33 37
Metric, positive definite 37
Michelson 53
Minkowski-space 177
Mode (normal) 26 29 42
Moller 6
Momentum 1 6 17 46 47 84 97 105 113 120 122 127 128 144
Momentum density 85 159
Momentum space 7 97 105 132
Momentum trajectory 105 106
Momentum, angular 6 19 47 82 120 121
Momentum, conservation of 18
Momentum, conservation of angular 82 121
Motion of a charged particle 183
Motion, aperiodic 116
Motion, central 120
Motion, charge 126 127
Motion, free 106 112
Motion, periodic 183
Multivector 61
Nature 8 12
Newton 46
Newton — Lorentz equation 128
Newtonian potential 150
Normalization 126
Normalization condition 136
Normalization, ortho 126 141
Number, Clifford 62 64ff 66 67 89
Number, hypercomplex 65
Observer 53 64 57 60 127
Observer, Galilean 63 58 68 81 83 87 90
Operator, divergence 87
Operator, gradient 72
Operator, vectorial 72
Operators, commutability of 76
Oscillator 27 57 100
Oscillator field 62 68 69 70 79 83 84 90 94 147
Oscillator Hamiltonian 141
Oscillator, harmonic 26
P-substitution 187
Packet 136
Packet, wave 140
PARAMETER 34 73
Parameter, independent 56
Parameter, inertia 42 44
Parity 187
Partition 56
Partition density 70
Partition, continuous 61
Partition, initial, function 198
PAST 56
Pauli 6
Peirce 139
Pendulum 16 22 95 107
Period 116
Period of time 116
Permutation 86 87 88 89
Phase 193
Phase agglomeration 113
Phase cell 196
Phase constant 26 26
Phase elements 165 192
Phase point 111 113 114 117
Phase space 97 104 113 117
Phase stream 198
Phase trajectory 105 106 111 113 114 116 193
Phase, pseudo, space 202
Phase, super, space 202
Picture 33 39 61
Picture, canonical 97
Picture, Einsteinian 54
Picture, incompressible-fluid 112
Picture, Lagrangian 9 39ff 41 42 47 53 54
Picture, Newtonian 9 39ff 41 42 47 53 54 55 97 191
Picture, phase 102
Picture, proper Newtonian 9 46
Picture, pseudo-Newtonian 9 42 46
Picture, Riemannian 39
Poincare 66 117
Poincare’s theorem 97 117 118
Poisson bracket 97 102 103 113 169 174
Poisson bracket-operator 102
Poisson equation 89
Postulate 54
Postulate, fundamental 12
Postulate, Newton’s 18
Potential 24 28 38 39 41 50 51 90 115 121 127
Potential density form 68 69 70 94
potential energy 11 23 27 39 40 60 97 115 120 122 123
Potential field 89
Potential, Coulombian 117
Potential, elastic 124
Potential, electric 51
Potential, electromagnetic 9 30ff 47 128
Potential, electrostatic 51
Potential, Fourier-analysis of the 126
Potential, gravitation 38 51
Potential, gravity 16
Potential, kinetic 9 41
Potential, Newtonian 39 51 117 160
Potential, retarded 132
Potential, scalar 31 124
Potential, time-dependent 97 125
Potential, vector 31 47 124 126 132
Potential, wave-packets of the 126
Power 51 117
Power series 50 93 123
Poynting 90
Poynting vector-density 92
Poynting’s expression 142
Preservation 52 80
Preservation of energy 144 168
Preservation of momentum 144 159
Preservative field 52 81 82 85 90 144 158
Product (scalar) 40 66
Quantization V
Quantum dynamics 102
Quantum electrodynamics 126 143
Quantum statistics 196
Quantum theory 196 210
Quasi-ergodicity 97 117
Radiation 3
Recommandations (international) 88
Reflexion, strong 189
Reflexion, weak 188
Relativity, classical 1 5
Relativity, general 6 9 37 38 39
Relativity, special 37 62 53 54 55 56 61 66 67 69 87 177
Retarded potential 132
Reversibility 165 174ff 181
Reversibility of dynamics 165 176
Reversibility of the first kind 176 182
Reversibility of the second kind 176
Reversibility, classical (or of the first kind) 176
Riesz 62
Rosenfeld 143
Rotation 58 63
Rotation (=curl) 70
Rotation, continuous 64
Savart 47
scalar 55 60 88
Scalar density 93
Scalar field 52 61 68 95
Scalar potential 124
Scalar product 40 66
Scalar, complex, field 144 160ff
Scalar, pseudo 61
Scalar, real, field 144 159ff
Schilt 88
Schroedinger’s equation 210
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