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Greiner W., Muller B., Rafelski J. Quantum electrodynamics of strong fields
Greiner W., Muller B., Rafelski J.  Quantum electrodynamics of strong fields









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: Quantum electrodynamics of strong fields

: Greiner W., Muller B., Rafelski J.

:

The fundamental goal of physics is an understanding of the forces of nature in their simplest and most general terms. Yet there is much more involved than just a basic set of equations which eventually has to be solved when applied to specific problems. We have learned in recent years that the structure of the ground state of field theories (with which we are generally concerned) plays an equally funda- fundamental role as the equations of motion themselves. Heisenberg was probably the first to recognize that the ground state, the vacuum, could acquire certain properties (quantum numbers) when he devised a theory of ferromagnetism. Since then, many more such examples are known in solid state physics, e. g. superconductivity, superfluidity, in fact all problems concerned with phase transitions of many-body systems, which are often summarized under the name synergetics.


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Absolute space      15
Action integral      194 472
Action principle      194
Adjoint spinor      29 52
Angular momentum barrier      64 75
Angular momentum coupling      308
Angular momentum operator      see Operator
Angular momentum tensor      223
Annihilation operator, electrons      219
Annihilation operator, positrons      220
Annihilation, electron-positron pair      see Pair annihilation
Anomalous magnetic moment      292 439
asymptotic freedom      527
Atomic clock      371
Atomic fine structure      95
Autocorrelation function      339
Autoionization formalism      13 123132 246
Autoionization formula      264
Autoionization process of positrons      see Projection formalism
Average screening potential      see Screening
Bag models      534535
Binding energy of a supercritical quasi-bound state      see Resonance energy
Binding energy of bosons in a Coulomb field      497498
Binding energy of electrons in a Coulomb field      85
Binding energy of quasi-molecular $1s\sigma$-state      310 355
Binding pockets in the internuclear potential      12 331 335 345 381388
Black hole      550 557563
Black hole, limiting charge of      557563
Black hole, limiting charge-to-mass ratio of      501
Bohr radius      353
Bohr Sommerfeld condition      458 461 559
Born series      177 179
Bose condensate      22 388 470 499 507519
Breit retardation function      435
Breit Wigner type distribution      136
Bremsstrahlung, nuclear or electronic      331 364
Canonical energy momentum tensor      see Energy momentum tensor
Canonical momentum      see Conjugate momentum
Canonical quantization      see Quantization
Casimir effect      6
Casimir energy      239
Centre-of-mass motion      13 375
Charge conjugation operator      see Operator
Charge conjugation symmetry      95105 226231 422
Charge conjugation transformation      228
Charge density operator      see Operator"
Charge renormalization      399402 (see also Renormalization)
Charge, critical      4 123
Charge, effective      7
Charge, overcritical      123
Charge, renormalized      402
Charge, subcritical      123
Charged vacuum      see Vacuum
chemical potential      232233
Christoffel symbol      550551
Chronological products      see Time ordering
Coincidence measurements      350 371
Collision      see also Heavy-ion collision
Collision time      303 330
Collision, elastic      353
Collision, inelastic      see Deep inelastic collision
Collision, supercritical      318 365388
Compton wavelength      278
Condensate equations      510519 533
Condensate equations, Bose condensate      533
Condensate equations, gluon condensate      533
Confinement of colour      524
Conjugate momentum      195 213
Conservation laws      197201
Conservation laws, angular momentum      see Poincare invariance
Conservation laws, charge      198 225
Conservation laws, energy momentum      see Poincare invariance
Conservation laws, parity      see Parity transformation"
Continuity equation      29 51 225
Continuum      see Energy solutions"
Continuum solutions of the Dirac equation      63 8691 150154
Continuum solutions of the Dirac equation, Coulomb field of extended nuclei      150154
Continuum solutions of the Dirac equation, Coulomb field of point nuclei      8691
Continuum solutions of the Dirac equation, square well potential      63
Continuum-continuum interaction      125 146
Conversion      12 362 374378
Conversion coefficients      357 376
Conversion lines      364
Conversion, excited nuclear states      12 362
Conversion, monoenergetic pair      377
Conversion, supercritical internal      10 386387
Correlation diagram      307 308
Coulomb barrier      313 330 370
Coulomb excitation      322 326
Coulomb phase      91
Coulomb phase shift      152 (see also Phase shift)
Coulomb scattering      330
Coulomb waves      see Continuum solutions
Coupling, constant electromagnetic      79 (see also Fine-structure constant)
Coupling, constant running      466 527528
Coupling, constant scalar      79
Coupling, constant strong      527
Coupling, dynamical      332
Coupling, gauge invariant      5658
Coupling, minimal      57 104 524
Coupling, scalar      67
Coupling, vector      68
Covariance of the Dirac equation      4146
Covariant angle-variables      50
Covariants, bilinear      5460
Creation operator, electrons      217
Creation operator, positrons      220
Critical distance      306 310312
Cross-section, delayed nuclear scattering      383384
Cross-section, nuclear reaction      380
Cross-section, Rutherford scattering      380
Current density, bare external      400401
Current density, Dirac particles      51
Current density, induced      400401 410
Current density, Klein Gordon particles      475
Current density, operator      229 (see also Operator)
Current density, renormalized      401 409
Current density, vacuum polarization      389390 (see also Vacuum polarization)
Decay of a supercritical K vacancy      264273
Decay of the neutral vacuum      273278 (see also Vacuum decay)
Decay time, supercritical bound state resonance      318
Decay time, supercritical K vacancy      136 264
Deep inelastic collision      330 370
Delbrueck scattering      16
Delta electrons      353356 (see also Heavy-ion collision)
Delta electrons, creation      354
Delta electrons, high energy      356
Delta electrons, scaling law      355356
Delta electrons, scaling plot      354355
Delta electrons, spectrum      353 377
Diagonalization, supercritical Dirac Hamiltonian      269271 (see also Projection formalism)
Diagrams, closed loops      392
Diagrams, corners      393
Diagrams, elementary processes      180182 206
Diagrams, self-energy      437438 442
Diagrams, vacuum polarization      367 392393
Diagrams, vertices and propagator of QCD      526
Dirac equation, coupled to electromagnetic fields      36
Dirac equation, fermions in a general metric      551
Dirac equation, free      2630
Dirac equation, MIT bag model      540 542
Dirac Hamiltonian      31 42
Dirac Hamiltonian, projected      126 (see also Projection formalism)
Dirac matrices      29
Dirac matrices, generalized      551
Dirac particles in a gravitational field      550557
Dirac sea      9296
Dirac's hole theory      35 92112
Dispersion integral representation      407 (see also Polarization function)
Displacement charge      133 (see also Vacuum polarization)
Distance of closest approach      314 353
Distribution function of nuclear reaction times      337338
Diving of a bound state      123132 (see also Resonance states in supercritical fields)
Doppler broadening      357 375376
Doppler shift      346 350 357
Double-resonance mechanism      385
Dynamical coupling      332 (see also Coupling)
Dynamically induced positron creation      331332 334 367
Dyson Schwinger equation      431
effective Lagrangian      see Heisenberg Euler Lagrangian
effective mass      7071
Effective potential      71 515 557
Effective temperature      23
Eigenfunction expansion of the Feynman propagator      see Feynman propagator
Einstein equations      199 552
Einstein Cartan theory      23
Electron bound state, atomic      8486
Electron bound state, quasi-atomic      302
Electron bound state, quasi-molecular      315316
Electron bound state, supercritical      250 265267 318
Electron scattering      190 (see also Thomas Fermi model)
Electron screening effects      310
Electron-electron interaction      321323 (see also Screening)
Electron-positron pair creation, induced      272 320
Electron-positron pair creation, real      181
Electron-positron pair creation, spontaneous      see also Vacuum decay
Electron-positron pair creation, virtual      see Vacuum polarization
Electronic transition in heavy-ion scattering      313
Energy momentum tensor, Dirac field interacting with an electromagnetic field      199200
Energy momentum tensor, free Klein Gordon field      474
Energy momentum tensor, gluon field      525
Energy momentum, four-vector      223
Energy solution, Dirac equation      3233 68 9295
Energy solution, Klein Gordon equation      477
Equal-time commutation relations for bosons      476
Equal-time commutation relations for fermions      214 216
Equilibrium state of the charged vacuum      233
Event horizon      557 560
Evolution of the vacuum state      257260
External field approach      200
Faddeev Popov ghosts      525
Fano's procedure      126 (see also Autoionization formalism)
Faraday effect      291
Fermi energy      3 233
Fermi level      343
Fermi momentum      446
Fermi surface      3 134 258 421 435
Feshbach Villars form      478
Feynman diagrams      see Diagrams
Feynman gauge      433
Feynman propagator free      209210
Feynman propagator, arbitrary strong external fields      235236 415
Feynman propagator, time-dependent fields      251256
Field equation, Dirac particles      31 36
Field equation, gluons      525
Field equation, gravitation      26 473 482 499; Klein
Field strength tensor, electromagnetic      522
Field strength tensor, QCD      524525
Fine-structure constant      1 2
Fine-structure formula      84 449
Fission of quark bags      540549
Fluctuations of the vacuum      2 435 512
Fock space fermions      23 218221
Fock space, bosons in external potentials      490 493495
Fock term      436
Fock Schwinger proper time method      538 (see also Proper time)
Friction model      371 (see also Deep inelastic collision)
Frictional force      330 (see also Friction model)
Fulling Unruh temperature      569
Furry picture      207 393
Furry theorem      393 423
Gamma matrices, standard representation      40
Gauge field      18 521524
Gauge groups      23 521524
Gauge independent coupling      see Minimal coupling
Gauge invariance      57 522524
Gauge transformation      see Invariance
Gell-Mann matrices      523
Gell-Mann Low theorem      441
Generating operator, finite Lorentz transformations      49
Generating operator, infinitesimal displacements      222
Generating operator, infinitesimal Lorentz transformations      222
Geometrodynamics      15
Giant molecule      146 (see also Quasimolecule)
Giant nuclear molecule      379 382
Gluon condensate      528534 (see also Condensate equation)
Gluons      523
Gravitational field      550
Gravitational field, static, spherically symmetric      551552
Green's function      415420 (see also Feynman propagator Dirac
Green's function, integral equation      423
Green's function, Maxwell equation      393
Green's function, partial wave decomposition      424426
Group operators      44 523
Group parameter      44 523
Hamilton's principle      473 (see also Action principle)
Hamiltonian density      196 474
Hamiltonian equations, bosons in external potentials      485
Hamiltonian for heavy-ion collision      322
Hamiltonian form      197
Hamiltonian formalism      195 213 495
Hamiltonian, critical      124
Hamiltonian, overcritical      124
Hamiltonian, subcritical      124
Hartree approximation      321
Hartree approximation, adiabatic time-dependent      321 342
Hartree Fock Slater approximation      321
Hawking effect      557
Head-on collision      300 314 370
Heavy-ion collision      7 300389
Heisenberg equation      214 257
Heisenberg operator      see Heisenberg picture
Heisenberg picture      213 215 273274
Heisenberg Euler Lagrangian      287 290291
Helicity      33
Hellmann Feynman theorem      318
Higgs field      20
Impact parameter      314 350352
In/Out formalism      see Evolution of the vacuum state
In/Out vacuum state      see Feynman propagator for time-dependent fields
Independent particle approximation      206
Induced positron creation      see Electron-positron pair creation
Inelastic scattering process      see Scattering
Infrared divergence      see Mass renormalization
Interaction between continua and boundstate      147; see Resonance in the continuum
Interaction, critical strength of      24
Interference effects in positron spectra      336
Internuclear potential pockets      331 381382
Internuclear potential, M3Y      381
Invariance properties of coupled fields      5658 102111 221230 522524
Invariance properties of coupled fields, charge conjugation symmetry      see Charge conjugation
Invariance properties of coupled fields, gauge transformation      5658 523524
Invariance properties of coupled fields, Lorentz transformation      3941
Invariance properties of coupled fields, parity transformation      5254 104106 230
Invariance properties of coupled fields, Poincare transformation      221224
Invariance properties of coupled fields, time reversal      106111
Ionization probability in perturbation theory      354 (see also Delta electrons)
K vacancy creation      352
K vacancy number operator      268 269
K-shell conversion      350
K-shell excitation      342
K-shell ionization      336 351 356
K-shell radius      353
Kinetic energy dissipation      330 (see also Deep inelastic collision)
Klein Gordon equation      see Field equation
Klein's paradox      17 112121 293299 467469
Lagrangian of QCD      524
Lagrangian of QED      194 522
Lamb shift      16 436
Landau energies      283
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