Observables, non-local field, orbital angular momentum of 111—113
Observables, non-local field, property of charge of 120
Observables, non-local field, quantum numbers relating to 118
Observables, non-local field, spin of 110—111
Observables, non-local field, total charge of 115—118 121
Observables, non-local field, vacuum state of 109
Observables, non-local field, variance of expectation values of 92—93
Observables, sets of commuting 43
Observables, sets of eigenvectors of 193—195
Observables, variance of expectation values of 204—206
Operator, charge parity 204
Operator, complete 14
Operator, creation and annihilation see "Creation and annihilation operators"
Operator, metric 262
Operator, Racah 218
Operators for state vector 46
Operators for state vector, properties of 47
Operators, field variables as 113—115
Operators, tensor product of 22
Operators, theorem for Hermitian 13
Operators, theorem for unitary 14
Orbital angular momentum in Dirac field 238
Orbital angular momentum of a field 111—113
Orbital angular momentum of arbitrary spin field 200
Orbital angular momentum, eigenvalues of 112
Orbital angular momentum, tensor 102—103 107
Parity of field 113—115
Parity of field and state vector 115
Particles, elementary and representation of Lorentz group 135—139
Particles, elementary, classification of 133—135
Particles, elementary, decay scheme of 134
Particles, elementary, differential operator of 144
Particles, elementary, Majorana 230
Particles, elementary, spin of 137 144
Particles, elementary, wave equation of 151
Particles, free 128—131
Particles, free, definition of 129
Particles, free, reduction postulate for wave equations of 130
Particles, free, wave equations of 159—160
Pauli matrices of Dirac equation 220
Pauli — Heisenberg quantization method 57
Pauli, exclusion principle 192—193
Peierls relation in variational formulation 90
Petiau — Duffin — Kemmer relation 145 278—281
Poisson bracket 19 20 24 60 61 63
Poynting vector 249
Proca — de Broglie equations 154
Proca — de Broglie field 270—281
Proca — de Broglie field, Lagrangian formulism and quantization of 272—273
Proca — de Broglie field, observables of 273
Proca — de Broglie field, Petiau — Duffin — Kemmer relations for 278—281
Proca — de Broglie field, Stueckelberg formulation for 273—275
Proca — de Broglie field, vector mesons of 271
Proca — de Broglie field, wave equations of 271—272
Proca — de Broglie field, wave mechanics of 275—278
Pseudo-scalar fields see "Scalar and pseudo-scalar fields"
Quantization in indefinite metric 262—267
Quantization of linear field equations 159-213
Quantization of linear field equations with constant coefficients 214—281
Quantization of linear field equations with constant coefficients and non-quantized Dirac equation 214—234
Quantization of linear field equations with constant coefficients and quantized Dirac equation 234—247
Quantization of linear field equations with constant coefficients in Maxwell field 247—270
Quantization of linear field equations with constant coefficients in Proca — de Broglie field 270—281
Quantization of spin 0 field see "Spin 0 fields"
Quantized field 103—109 110—118
Quantized field, action of 103
Quantized field, current vector of 116
Quantized field, energy momentum conservation of 107
Quantized field, orbital angular momentum of 111—113
Quantized field, parity of 113—115
Quantized field, Schwinger — Feynman variational principle and 104
Quantized field, spin of 110—111
Quantized field, symmetrical energy-momentum tensor of 108
Quantized field, total angular momentum of 109
Quantized field, total angular momentum operator of 105 107
Quantized field, total charge of 115—118
Quantized field, total momentum operator of 105 107
Quantized field, vacuum state of 109
Quantizing a field xiii 40
Quantum electrodynamics, basic ideas of xvii—xx
quantum mechanics 23—27
Quantum mechanics, classical mechanics and 24
Quantum mechanics, maximal measurement of 25
Quantum mechanics, origins of 23
Quantum mechanics, Schroedinger — Heisenberg pictures in 26—27
Quantum system and classical equivalent 42
Quantum system, description by classical system of 74
Racah operator 218
Reduction postulate for wave equations 130 142—146
Scalar and pseudo-scalar fields 160—184
Scalar and pseudo-scalar fields, commutation rules 182
Scalar and pseudo-scalar fields, field equations of 183
Scalar and pseudo-scalar fields, non-Hermitian 174—181
Scalar and pseudo-scalar fields, non-Hermitian, energy-momentum tensor of 175 180
Scalar and pseudo-scalar fields, non-Hermitian, number operator of 176 179—181
Scalar and pseudo-scalar fields, quantization of Hermitian 171—174
Scalar and pseudo-scalar fields, vacuum-expectation values of 183—184
Scalar and pseudo-scalar fields, various solutions of wave equations of 160—170
Scalar and pseudo-scalar fields, various solutions of wave equations of, table of functions of 163—167
Scalar and pseudo-scalar fields, wave equation of 160
Schroedinger equation 26
Schroedinger picture xv 26—27
Schroedinger picture for canonical transformation 77—79
| Schroedinger picture, Hamiltonian equation for 27
Schur lemma 202 216
Schwinger — Feynman variation principle 79—88
Schwinger — Feynman variation principle on quantized field with invariant action 104—105
Schwinger — Feynman variation principle with arbitrary variation 81—83
Schwinger — Feynman variation principle, canonical equation from 86
Schwinger — Feynman variation principle, definition of 79—80
Schwinger — Feynman variation principle, Hermitian action of 79
Schwinger's method of evaluating wave equation functions 170
Space symmetry 113—115 206—207 218—220
Space symmetry, behaviour of Dirac field under 242—243
Space-like surfaces 6—8
Space-like surfaces, commuting of variations on 83—84
Space-like surfaces, condition for equitemporal plane on 7
Space-like surfaces, effect on Lorentz transformation of 6
Space-like surfaces, functionals of 35—36
Space-like vector 45
Space-time points 37
Space-time points and evolution of field variables 51
Space-time points and variation of field variables 84—86
Space-time points, measurement of electric field at 270
Space-time translation operator 52 53 69—70
Spin 155—156
Spin 0 fields 159—184
Spin 0 fields, commutation rules for 182
Spin 0 fields, field equation of 183
Spin 0 fields, non-Hermitian 174—181
Spin 0 fields, quantization of Hermitian 171—174
Spin 0 fields, solution of wave equations of 160—170
Spin 0 fields, vacuum-expectation values of 183—184
Spin 0 fields, wave equation of 160
Spin field 144
Spin field, arbitrary see "Arbitrary spin fields"
Spin field, commutation relations of Dirac matrices of 144
Spin field, summation over 231—233
Spin field, tensor components of wave function of 153—155
Spin of a field 110—111
Spinors, Dirac 226—228
Spinors, Majorana 230
State vector and parity of field 115
State vector for Hermitian scalar field 194
State vector in Heisenberg picture 43
State vector of linear space 35
State vector of non-zero spin field 113
State vector of zero spin field 112—113
State vector, calculation of observables by 44
State vector, effect of interacting fields on 159
State vector, evolution of 45—50
State vector, independence of norm of 45
State vector, operators of 46
State vector, operators of, properties of 47
Stueckelberg formulation 273—275
Summations over spins 231—233
T.C.P. theorem 212 247
Taylor's formula for functionals 35
Tensor products, formulae for 22
Tensor, classical energy-momentum 101—103
Tensor, classical energy-momentum, law of conservation of 102
Tensor, components of wave functions 153—154
Tensor, orbital angular momentum 102—103 107 200
Tensor, symmetrical energy-momentum 108
Tensor, total angular momentum 107 109
Time reversal 207—213
Time reversal and total charge of field 210—211
Time reversal by antilinear transformation 208
Time reversal of Dirac equation 218—219
Time reversal, commutation rules of 209—210
Total charge of field 115—121
Total charge of field and charge conjugation 121
Total charge of field and time reversal 210—211
Total charge of field of arbitrary spin field 204—206
Total charge of field, eigenvector of 120
Unitary operator and parity of fields 113—115
Unitary operator as charge parity operator 204
Unitary operator for definition of time reversal 212
Unitary operator for state vector 46
Unitary operator of quantized field 105
Unitary operator, generation of canonical transformation by 75
Unitary operator, properties of 47
Unitary operator, theorem for 49
Vacuum expectation values of field variables 172—174
Vacuum expectation values of field variables of Dirac field 244—245
Vacuum state of field observables 109
Vacuum state of field observables, fermion propagator of 245
Variation formulation 79—90
Variation formulation, commutation relations in 86—88
Variation formulation, local character of field equation by 88—90
Variation formulation, Peierls relation for 90
Variation formulation, Schwinger — Feynman variation principle of 79—88
Variation formulation, structure of Hamiltonian of 88—90
Vectors, bra 12
Vectors, difference between space-like and timelike 5
Vectors, ket 12
Vectors, Poynting 249
Vectors, wave propagation of 9
Wave equation of interacting fields 159
Wave equation of particles of spin 0 160
Wave equation of particles of spin 0, elementary solutions of 160—170
Wave mechanics of Proca — de Broglie field 275—278
Wave propagation vector 9
Wigner — Bargman classification of particles 130 135—139
Wigner's procedure for matrix representation 197
Wigner's suggestions on time reversal 208
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