Adjoint of field variables 147 150 174—177
Adjoint operator for Maxwell field 263—264
Annihilation operators see "Creation and annihilation operators"
Arbitrary spin fields, anticommutation rules of 188
Arbitrary spin fields, charge conjugation of 201—206
Arbitrary spin fields, commutation rules of 185—187 192—193
Arbitrary spin fields, drawbacks of Hamiltonian formalism in 184—187
Arbitrary spin fields, energy momentum tensor of 200
Arbitrary spin fields, observables of 189—192 199—201
Arbitrary spin fields, reduced operators of 189—192
Arbitrary spin fields, sets of eigenvectors of observables of 194—195
Arbitrary spin fields, space symmetry of 206—207
Arbitrary spin fields, time reversal of 207—213
Arbitrary spin fields, total charge operator of 204—206
Arbitrary spin fields, variance of expectation values in 204—206
Arbitrary spin fields, wave equation of 189
Bargman — Wigner method 130 135—139
Bohr's correspondence principle 24
Bose — Einstein statistics 192—193
Boson fields 84 133—136 197 203
Breuler's theory for indefinite norm 262
Canonical formalization of quantum field theory 79—86
Canonical systems, classical equivalents of 57—73
Canonical systems, definition and properties of 51—57
Canonical systems, field equations in 53
Canonical systems, space-time translation operator in 52 53 69—70
Canonical transformations and Lorentz transformation of wave equation 148
Canonical transformations and parity of field 114—115
Canonical transformations and time reversal 212
Canonical transformations on linear spaces 17—19
Canonical transformations, charge conjugation of 91 120—121
Canonical transformations, Foldy — Wouthuysen transformation of 233—234
Canonical transformations, general principles of 73—74
Canonical transformations, generated by unitary operator 75
Canonical transformations, Heisenberg picture for 74—75
Canonical transformations, Schroedinger picture for 77—79
Causality principle 43
Charge conjugation and Lorentz group 206
Charge conjugation for Dirac equation 229—230 242—244
Charge conjugation of arbitrary spin fields 201—206
Charge conjugation, determination of commutation by 203—204
Charge conjugation, transformation 91 120—121
Charge parity operator 204
Classification of elementary particles 133—135
Clebsch — Gordan theorem 143 152
Compton wavelength 9—11
Contravariant spinor 223
Creation and annihilation operators 121—127
Creation and annihilation operators and Lorentz transformation 121—122
Creation and annihilation operators for fields of arbitrary spin 191—192
Creation and annihilation operators for Maxwell field 256—258
Creation and annihilation operators for non-Hermitian scalar field 179
Creation and annihilation operators of Dirac field 239—244
Creation and annihilation operators of Hermitian scalar field 193
Creation and annihilation operators, construction of representation of 195—199
Creation and annihilation operators, effect on eigenvalue of 121
de Broglie fusion method 130 151—158
de Broglie fusion method, basic idea of 151
de Broglie — Proca equations 154
Dirac equation, non-quantized and Lorentz invariance 217—219
Dirac equation, non-quantized, algebra of Dirac matrices of 214—217
Dirac equation, non-quantized, charge conjugation for 229—230
Dirac equation, non-quantized, Feynman notation for 228—229
Dirac equation, non-quantized, Foldy — Wouthuysen transformation in 233—234
Dirac equation, non-quantized, Majorana spinors of 230
Dirac equation, non-quantized, monochromatic plane wave solution of 223—228
Dirac equation, non-quantized, Pauli matrices for 220
Dirac equation, non-quantized, representation of matrices of 220—223
Dirac equation, non-quantized, spin operator of 217 224
Dirac equation, non-quantized, standard representation for 222 225
Dirac equation, non-quantized, summations over spins and energies in 231—233
Dirac equation, non-quantized, transformation laws of tensor expressions of 219—220
Dirac equation, quantization of, anticommutation rules of 236—238
Dirac equation, quantization of, charge conjugation of 242—244
Dirac equation, quantization of, creation and annihilation operators of 239—244
Dirac equation, quantization of, Dirac field observables of 238—239
Dirac equation, quantization of, elementary solutions of 234—236
Dirac equation, quantization of, fermion propagator of 245
Dirac equation, quantization of, Foldy — Wouthuysen transformation in 241
Dirac equation, quantization of, Hamiltonian for 236—238
Dirac equation, quantization of, non-conservation of parity in 245—247
Dirac equation, quantization of, particle properties of 239—244
Dirac equation, quantization of, solution by evolution wave operator of 237
Dirac equation, quantization of, spinor in 242—243
Dirac equation, quantization of, vacuum expectation values of 244—245
Dirac field, application of observables to 201
Dirac field, behaviour under space symmetry of 242—248
Dirac field, conjugation matrix for 204
Dirac field, invariance of 92 150
Dirac field, investigation of non-quantized Dirac equation in 214—234
Dirac field, investigation of quantized Dirac equation in 234—247
Dirac field, observables of 238—239
Dirac function 15
Dirac function with one-dimensional argument 28
Dirac Hamiltonian in wave mechanics 224
Dirac Hamiltonian in wave mechanics, diagonalization of 233—234
Dirac spinors as degenerate eigenvectors 228
Dirac spinors, orthonormal system of 227—228
Duffin — Petiau — Kemmer relation 145 278—281
Einstein's formula 9
Euler's constant 170
Evolution operator and canonical pictures 75
Evolution operator of field variables 51
Evolution operator of state vector 46
Evolution operator, properties of 47 52
Evolution operator, theorems on 52—53
Fermi condition for Maxwell field 255 259—262
Fermi — Dirac statistics 192—193
Fermion fields 84 195 203
Feynman notation for Dirac equation 228—229
Field equations for quantum-classical theory 64—67
Field equations, differential operator of 142—146
Field equations, differential operator of, anticommutation rules by 188
Field equations, differential operator of, commutation rules by 185—187
Field equations, differential operator of, elementary solution of 189
Field equations, Hamiltonian form of 58—63
Field observables see "Observables"
Field variables 42
Field variables and displacement of time-space points 84—86
Field variables and Hamiltonian density 88—90
Field variables and one-particle states 129
Field variables as complete ring of operators 80—82
Field variables as operators 113—115
Field variables of non-Hermitian fields 174—181
Field variables of non-Hermitian fields in terms of reduced operators 178
Field variables of scalar field 172
Field variables, application of variation principle on 79—88
Field variables, commutation rules by change of 185—187
Field variables, commutation rules for various times of 70—72
Field variables, commutation rules in Proca — de Broglie field of 272
Field variables, evolution of 51—54
Field variables, Hamiltonian form of field equations of 58—63
Field variables, local commutativity of 56—57
Field variables, mathematical definition of 54—55
Field variables, microcausality of 56—57
Field variables, non-Hermitian operators of 72—73
Field variables, Peierls relation for commutator of 90
Field variables, space-time translation operator of 52 53 69—70
Field variables, vacuum expectation values of 172—174 181
Fields and quantum description 41—45
Fields of arbitrary spin see "Arbitrary spin fields"
Fields of spin 0 see "Spin 0 fields"
Fields, investigation of electro-magnetic 41—42
Fields, local 41—42
Foldy — Wouthuysen transformation 233—234 241
Fourier transformation and creation and annihilation operators 124—125
Fourier transformation for one-dimensional variable 28
Fourier transformation of convolution product 29
Fourier transformation on wave equation 148
Free fields xiv 81
| Free fields, one-particle state in 129
Free photon field see "Maxwell field"
Functional analysis, basic notations of 32—39
Functional analysis, calculus of variations of 37—39
Functional of a functional 36—37
Functional of space-like surfaces 35—36
Functional, definition of derivative of 33
Functional, derivative of linear 34
Functional, Gauss's theorem for 35
Functional, Green's theorem for 36
Functional, Taylor formula for 35
Gauge group 115—127
Gauge group, definition of total charge by 115—118
Gauge transformation of Maxwell equations 252—253
Gauss's theorem 35 83
Green functions 161 235
Green's theorem 36 61
Gupta's theory for indefinite norm 262
Heisenberg picture xv 25 26—27 43 44
Heisenberg picture for canonical transformation 74—77
Heisenberg picture for Maxwell field 255
Heisenberg picture, Hamiltonian density in 76—77
Heisenberg picture, Hamiltonian equations for 27
Heisenberg picture, observables in 91
Heisenberg picture, particle with spin 0 in 112—113
Heisenberg picture, state vector in 43 46
Heisenberg — Pauli quantization method xiii 57
Helicity by Stokes parameters 224
Hilbert space 16 20 24 25 32 41 42 46 50
Interacting fields xv 159
Interacting fields, wave equations of 159
Interaction picture xvi
Invariance of Maxwell equations 92
Invariance of quantum field theory 92—94
Invariance of wave equations 139—142
Jacobi identity 19
Kemmer — Petiau — Duffin relation 145 278—281
Klein — Gordon equation 129
Klein — Gordon equation, probability density in 156
Law of force in special relativity 8
Lie algebra 19
Lie equations for field observables 99
Lie formula 97
Lie formula for representation of Lorentz group 99
Lienart and Wiechert formulae 249
Linear field equations with constant coefficients 159—213
Linear field equations with constant coefficients for arbitrary spin fields see "Arbitrary spin fields"
Linear field equations with constant coefficients for scalar and pseudo-scalar fields see "Scalar and pseudo-scalar fields"
Linear wave equations 128—158
Linear wave equations and action 146
Linear wave equations and Lorentz group 135—150
Linear wave equations for particle of spin S/2 151—153
Linear wave equations under Fourier transformation 148
Linear wave equations, adjoint of 147 150
Linear wave equations, expectation value of energy of 157—158
Linear wave equations, field equation of 142
Linear wave equations, general data on 135
Linear wave equations, Hermitian character of 146—150
Linear wave equations, norm of 157—158
Linear wave equations, probability density of 156—157
Linear wave equations, quantization of see "Quantization of linear wave equations with constant coefficients"
Linear wave equations, reduction postulate for 130 142—146
Linear wave equations, relativistic invariance of 139—141
Linear wave equations, tensor components of spin fields 153—155
Linear wave equations, theorem on spin and 144
Local fields 41—42
Lorentz group 1—6 91 115
Lorentz group and charge conjugation 206
Lorentz group and Dirac equation 218—219
Lorentz group and Lie formula 99
Lorentz group and particles 129 135—139
Lorentz group and wave equations 135—150
Lorentz group, four classes of 3
Lorentz group, generation by special group of 3
Lorentz group, group representation of 95 128—129
Lorentz group, irreducible representation of 128 135—137
Lorentz group, multiplication law of 94—95
Lorentz group, unitary representation of 97
Lorentz invariance 92
Lorentz invariance and non-quantized Dirac equation 217—219
Lorentz invariance for particles with spin 0 168
Lorentz invariance of a theory 93
Lorentz transformation and canonical transformation 149
Lorentz transformation and invariance of wave equation 139—140 148
Lorentz transformation for particles with spin 0 165
Lorentz transformation on components of spinor 152
Lorentz transformation, "light cone" of 4
Lorentz transformation, antichronous subgroup of 3
Lorentz transformation, condition for 2
Lorentz transformation, creation and annihilation operators and 121—122
Lorentz transformation, effect on scalars of 5
Lorentz transformation, effect on space-like surfaces of 6
Lorentz transformation, effect on wave function of 95—97
Lorentz transformation, homogeneous 95—96 97
Lorentz transformation, homogeneous, variance of variables under 95
Lorentz transformation, inhomogeneous 94—101
Lorentz transformation, inhomogeneous, definition of 94
Lorentz transformation, inhomogeneous, effect on quantized field of 103—106
Lorentz transformation, Lie equation for representation of 99
Lorentz transformation, orthochronous subgroup of 3
Lorentz transformation, parity and invariance under 113—115
Majorana spinors 230
Matrix mechanics see "Quantum mechanics"
Maximal measurement of observables 25
Maximal measurement of spin of particle 150
Maxwell equations, description of electric field by 248
Maxwell equations, elementary solution of 254
Maxwell equations, four-dimensional formulation of 250—251
Maxwell equations, Gauge transformation on 252—253
Maxwell equations, three-vector formulation of 250—251
Maxwell field 247—270
Maxwell field, classical Maxwell equation in 248—252
Maxwell field, commutation rules of 256
Maxwell field, continuity equation of 248
Maxwell field, creation and annihilation operators on 256—258
Maxwell field, Fermi condition for 255 259—262 265 266
Maxwell field, Heisenberg picture of 255
Maxwell field, Hermitian operator for 263—264
Maxwell field, Lagrangian formalism and quantization of 254—258
Maxwell field, longitudinal and scalar photons in 258 259—261 266—267
Maxwell field, measurement of electric and magnetic fields of 270
Maxwell field, metric operator for 262
Maxwell field, observables of electro-magnetic fields of 267—269
Maxwell field, quantization in indefinite metric 262—267
Natural unit system 8—12
Natural unit system, conversion table to C.G.S. system 11
Natural unit system, simplification of formulae in 10
Non-local field observables see "Observables"
Notation xxi
Notation, concerning linear spaces 12—22
Observables xiii 40 46
Observables and causality principle 43
Observables and invariance of wave equation 142
Observables as constants of motion 74
Observables of arbitrary spin fields 189—192
Observables of Dirac field 238—239
Observables of electro-magnetic field 267—269
Observables of field 199—201
Observables of field of wave equation 149
Observables of Proca — de Broglie field 273
Observables of scalar fields 171—174
Observables, eigenvalue of 43
Observables, expectation values of 44 73—74
Observables, non-local field and parity 113—115
Observables, non-local field under Lorentz transformation 94—101
Observables, non-local field with invariant action 103—109
Observables, non-local field, definition of 91
Observables, non-local field, eigenvalue of 121—127
Observables, non-local field, eigenvectors of 118—120
Observables, non-local field, Lie equations for 99
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