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Schwinger J. — Particles, Sources, And Fields. Volume 3

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Название: Particles, Sources, And Fields. Volume 3

Автор: Schwinger J.

Аннотация:

An extension of Dr. Schwinger's two previous classic works, this volume (the 3rd of 3) contains 4 sections in addition to the previous sections of Electrodynamics II, which were concerned with the 2-particle problem, & applications to hydrogenic atoms, postronium, & muonium. Paper.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 318

Добавлена в каталог: 31.10.2010

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Предметный указатель

Absolute simultaneity      2
action      see also "Action principle"
Action coupling two electromagnetic fields through single fermion pair exchange, $W^{(2)}$       251
Action for neutral pion coupling to photons      295
Action in para positronium      133
Action principle      25 see
Action principle for two-particle interacting non-relativistic system      9
Action principle, using equal time fields      12
Action, $W^{(2)}$ , modified by single virtual photon exchange, $W^{(4)}$       252
Action, $W^{(2)}$ , non-causal evaluation of      263
Action, $W^{(4)}$ , contact term in      253
Action, $W^{(4)}$ , structural analysis of      254
Action, associated with single photon exchange      145
Adler, S.      298
Amplitudes, of mixed ortho-para positronium states      127
Analogy with time development      145
Angular momentum, and spin $\frac{1}{2}$ particles      54
Annihilation coupling, in ortho positronium      126
Anomaly, in pion decay into photons      298
Axial vector      67
Bessel function, of imaginary argument, $K_{nu}$       180
Bound state, as a composite particle      22
Breit interaction energy      38
C      114 see
Causal arrangement, for two-particle interaction description      30
Causal control and unstable particles      91
Causal control in two-particle exchange      91
Causal Diagram, for pion decay into photons      292
Charge parity of n-photon state      113
Charge parity of n-photon state in positronium      113
Charge reflection and a selection rule      112
Charge reflection, eigenvectors of      112
Completeness, of eigenfunctions      15
Composite particle, and statistics      24
Contact terms for $M^{(2)}$       198
Contact terms for pseudoscalar coupling      301
Contact terms for pseudovector, coupling      302
Contact terms for pseudovector, dynamical modification      305
Contact terms for pseudovector, relationship with electromagnetic parameter      303
Contact terms for strong field calculation      150
Contact terms, fiction associated with      152
Contact terms, locality of      197
Convergence factor      302
Coordinates, center of mass      13
Coordinates, relative      13
cp      114
Current algebra      297 298 306
Current, transverse, symbolic construction of      36
De Raad, L.      299
Decay constant for magnetic dipole radiation      171 174
Decay constant in magnetic field, at high energy      182
Decay constant of para positronium state      133
Decay constant of state in a magnetic field      168
Decay rate, of mixed ortho-para positronium state      127
Derivative, functional      24
Determinant, differential property of      149
Diamagnetic term, in mass operator      171
Divergence equation      77
Divergences      140
Double commutator, identity for      216
Effective charge, in asymptotic photon propagation function      280
Eigenfunctions      14 see
Eigenfunctions and Green's function construction      15
Eigenfunctions, completeness property of      15
Eigenfunctions, differential equation for      15
Eigenfunctions, including center of mass motion      16
Eigenfunctions, multi-time      17
Eigenfunctions, multi-time and orthonormality      18
Eigenfunctions, multi-time, differential equations for      17
Eigenfunctions, multi-time, physical interpretation of      18
Eigenfunctions, orthonormality of      15
Electrodynamics, narrow sense of      112
Energy displacement      see also "Energy shift" "Mass displacement
Energy displacement of order $\alpha(m/M)$ , for Coulomb interaction      55
Energy displacement of order $\alpha(m/M)$ , relative to fine structure      55
Energy displacement of order m/M for 2p level      69
Energy displacement of order m/M for 2s level      67
Energy displacement of order m/M, estimate for      71
Energy displacement, additional, in ortho positronium      125
Energy displacement, apparent discrepancy in      58
Energy displacement, effect of modified vacuum polarization on      108
Energy displacement, high frequency, of order m/M      67 69
Energy displacement, low frequency, of order m/M      65 74
Energy displacement, positronium      see "Ortho-para splitting"
Energy displacement, relative of 2s and 2p levels      80 109
Energy displacement, relative of ortho and para levels      125 126
Energy displacement, relative, modified, of ortho and para levels      140
Energy of ground state in strong fields      164
Energy operator of para positronium      122
Energy operator, Dirac, transformed      52
Energy operator, internal, non-relativistic      47
Energy operator, non-relativistic, of positronium      123
Energy operator, positronium, submatrix of      127
Energy operator, rest frame, of positronium      122
Energy operator, two-particle in rest frame      48
Energy operator, two-particle with large mass ratio      48
Energy operator, two-particle, approximately relativistic      46
Energy shift      see also "Energy displacement"
Energy shift for instantaneous Coulomb interaction      63
Energy shift for non-local interaction      61
Energy shift of order m/M for 2p level      79
Energy shift of order m/M for 2s level      79
Energy shift of order m/M, one-photon exchange      78
Energy shift of order m/M, unit for      79
Energy shift, technique for evaluating      76
Energy spectrum in magnetic field      157
Energy spectrum in magnetic field with $\alpha/2\pi$ magnetic moment      159
Energy spectrum, one-particle, approximately relativistic      51
Energy spectrum, relativistic, for spin 0 particle      54
Energy spectrum, single particle, from second order Dirac equation      53
Energy spectrum, total momentum dependence of      46
Energy spectrum, two-particle and reduced mass      52
Energy spectrum, two-particle with large mass ratio      50
Energy spectrum, two-particle, expectation values for      49
Energy spectrum, two-particle, first relativistic corrections to      44
Energy splitting, ortho-para, modification of      128
Energy, kinetic, non-relativistic decomposition of      14
Equations of motion, non-relativistic      68
Equations of motion, solution for constant field      146
Equivalence between pseudoscalar and pseudovector couplings      286
Euclidean metric, in momentum space      287 289 290 291 305 308
Euler's dilogarithm      95
Euler's dilogarithm, applications of      97
Exponentials, theorem on combination of      204
Factor, modifying pion-photon coupling      299 305
Feynman diagram      see "Non-causal diagram"
Field, difference      9
Field, multi-time, equal time specialization of      2
Field, single particle, non-relativistic      2
Field, source of      10
Field, two-particle non-interacting, non-relativistic      2
Field, two-particle, differential equation for      7
Field, two-particle, equal time      4
Field, two-particle, equal time, differential equation for      4 8
Fine structure      50
Fine structure and reduced mass      52
Fine structure in positronium      112
Fine structure, constant value of      250
Form factor and causal control      91
Form factor for pseudoscalar coupling      301
Form factor in neutral pion coupling to photons      295
Form factor in photon weight function      111
Form factor in three-photon decay of positronium      118
Form factor, causal diagram for      195
Form factor, charge and magnetic, for scattering, as checks      220
Form factor, effective, in ortho-para splitting      129
Form factor, non-relativistic, as wave function      100
Form factor, spin $\frac{1}{2}$ in vacuum polarization calculation      105
Functional derivative      24
Functional derivative as symbolic photon source      29

Functional derivative of Green's function      75
Gauge invariance and tensor structure      86
Gauge invariance and Ward's identity      207
Gauge invariance as a check of algebra      206
Gauge invariance, maintenance of      288
Generating function of s-states      66
Generating function, energy spectrum, physical information in      36
Generating function, for energy spectrum      35
Green's function      see also "Propagation function"
Green's function for immobile particle, and photon source      33
Green's function, advanced      42
Green's function, approximate equal time equation for with non-local interaction      60
Green's function, change of order m/M, through single photon exchange      77
Green's function, composition property for      77
Green's function, effective single particle      77
Green's function, eigenfunction construction of      15
Green's function, equal time, differential equation for      3
Green's function, equal time, symbolic construction of      26
Green's function, factorized      14
Green's function, functional derivative of      24 27 32 75
Green's function, identical particle symmetry of      28
Green's function, multi-time and equal time, relation of      3
Green's function, multi-time, eigenfunction expansions of      16
Green's function, multi-time, integral equations for      20
Green's function, multi-time, symbolic construction of      24
Green's function, multi-time, unified expression for      20
Green's function, non-relativistic version of      75
Green's function, relativistic with instantaneous interaction      38
Green's function, retarded      40
Green's function, single particle, relativistic, equal time limit of      39
Green's function, spin $\frac{1}{2}$       145
Green's function, transformed, boundary condition for      43
Green's function, transformed, differential equation for      41
Green's function, transformed, sets of equations for      42
Green's function, two-particle, differential equation for      7
Green's function, two-particle, equal time, differential equation for      8
Green's function, two-particle, non-interacting, relativistic      30
Green's function, unitary transformation of      40
Ground state energy in strong magnetic fields      164
Ground state in magnetic field      157
Hard core sourcery      284
Harold on "regularization"      268
Harold on a comparison with experiment      144
Harold on a conceptual and computational improvement      140
Harold on comparison of causal and non-causal methods      278
Harold on magnetic moment calculations      251
Harold on surface integrals      289
Harold on the asymptotic behavior of the photon spectral weight function      278
Harold on the existence of an integral      138
Harold on the expectation value of $\gamma^{0}$       158
Harold on the quantum correction to synchrotron radiation      187
Harold on the vacuum polarization calculation      110
Harold on Ward's identity      207
Heaviside step function      167
Heavy photons      140
Hyperfine structure in positronium      112
Hyperfine structure of muonium      140
Hyperfine structure, interaction for      48
Infinite momentum frame, and three-particle kinematical integral      82
Infra-red cutoffs      140
Infra-red problem, mathematical origin of      162
Interaction energy of positronium with magnetic field      126
Interaction energy, additional, of order m/M      64
Interaction energy, Coulomb      34
Interaction energy, instantaneous      38
Interaction energy, transformed, approximation to      45
Interaction energy, transformed, submatrices of      41
Interaction function, non-relativistic, property of      6
Interaction, additional, of order m/M      70
Interaction, non-local, Green's function treatment of      58
Interaction, phenomenological, for para positronium decay      116
Jackiw, R.      298
K'ung Fu-tzu      268
Karplus, R.      140
Klein, A.      140
Lorentz gauge      260 268 270 273
Magnetic field, energy spectrum and eigenfunctions in      156
Magnetic field, strong      144
Magnetic Moment contact term, contribution to $(c_{2})^{''}_{\delta}$       249
Magnetic Moment contact term, contribution to $(c_{2})^{'}_{\delta}$       238
Magnetic Moment contact term, contribution to $(c_{2})_{\alpha}$       223
Magnetic Moment contact term, contribution to $(c_{2})_{\beta}$       225
Magnetic Moment contact term, contribution to $(c_{2})_{\gamma}$       225
Magnetic Moment contact term, contribution to $(c_{2})_{\zeta^{''}}$       199
Magnetic Moment, causal diagrams for      195
Magnetic Moment, comparison with experiment      250
Magnetic Moment, induced      163
Magnetic Moment, labor saving devices for      235
Magnetic Moment, modified propagation function contributor to $(c_{2})_{\bar{G}}$       194
Magnetic Moment, non-causal diagram for      195
Magnetic Moment, numerical coefficient of $(\alpha/2\pi)^{2}$       250
Magnetic Moment, strong field modification of      178
Magnetic Moment, three particle exchange process in      194
Magnetic Moment, vacuum polarization correction to, $(c_{2})_{v.pol}$       190 191
Magnetic polarization      163
Magnetic polarization, strong field modification of      178
Mass operator $M_{0}$ , construction of      201
Mass operator $M_{1}$ , non-causal calculation of      257
Mass operator $M_{1}$ , presentation of      262
Mass operator for single photon exchange, M      197
Mass operator for strong field calculation      155
Mass operator for two photon exchange $M^{(2)}$       196
Mass operator M, decomposition into $M_{0}+M_{1}$       200
Mass operator M, tests of contributions to      263
Mass operator magnetic field for energy state      165
Mass operator magnetic field for first excited level in      171
Mass operator magnetic field for ground state      160
Mass operator magnetic field to quadratic terms for      170
Mass operator magnetic field, imaginary part of      167
Mass operator magnetic field, imaginary part, at high energy      180
Mass operator remainder, $M_{1}^{(2)}$       201
Mass, displacement of, in ortho positronium      126
Mass, displacement of, in para positronium      133 135
Mass, displacement of, reduced      14
Mass, displacement of, spectral restrictions on      83
Mathematical addendum, direct calculation of relation between pseudovector and electromagnetic contact terms      308
Matrix element, in ortho-para positronium transition      127
Milton, K.      299
Momenta, center of mass      13
Momenta, relative      13
Multi-photon processes      28
Multiparticle exchange      1
Muonium      48
Muonium and weak interactions      112
Muonium, hyperfine splitting, a contribution to      143
Muonium, hyperfine splitting, agreement with experiment      144
Muonium, hyperfine splitting, non-relativistic formula for      143
Muonium, two-photon exchange in      140
Neutrino, in muonium decay      112
Newton, R.      178
Non-causal diagram for magnetic moment      195
Non-overlap, in non-causal calculation      291
Normalization conditions for $M_{0}$       151
Normalization conditions for pseudoscalar coupling      301
Orbital quantum number, for positronium      112
Ortho positronium      114
Ortho-para splitting, complete modification of single-photon annihilation contribution to      130
Ortho-para splitting, contributions to      139
Ortho-para splitting, form factor modification of      130
Ortho-para splitting, modification in annihilation contribution to      129
Orthonormality of multi-time eigenfunctions      18
Oscillator, one-dimensional      157
P      114 see
Para positronium      114
Parity charge      113
Parity space      113
Parity, intrinsic      113
Parity, orbital      113
Particle, composite, and phenomenological description      22
Particle, identical      28

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