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ОбложкаKeller O. Light: the physics of the photon. - Boca Raton: CRC press/Taylor & Francis , 2014. - xix, 462 p.: ill. - (Series in optics and optoelectronics). - Bibliogr.: p. 429-439. - Ind.: p.441-462. - ISBN 978-1-4398-4043-6
Шифр: (И/В34-K31) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ...................................................... xiii
Acknowledgments ............................................... xix
About the author .............................................. xxi

I  Classical optics in global vacuum ............................ 1
1  Heading for photon physics ................................... 3
2  Fundamentals of free electromagnetic fields .................. 7
   2.1  Maxwell equations and wave equations .................... 7
   2.2  Transverse and longitudinal vector fields ............... 8
   2.3  Complex analytical signals ............................. 10
   2.4  Monochromatic plane-wave expansion of the
        electromagnetic field .................................. 13
   2.5  Polarization of light .................................. 14
        2.5.1  Transformation of base vectors .................. 14
        2.5.2  Geometrical picture of polarization states ...... 15
   2.6  Wave packets as field modes ............................ 18
   2.7  Conservation of energy, moment of energy, momentum,
        and angular momentum ................................... 21
   2.8  Riemann-Silberstein formalism .......................... 22
   2.9  Propagation of analytical signal ....................... 24
3  Optics in the special theory of relativity .................. 27
   3.1  Lorentz transformations and proper time ................ 27
   3.2  Tensors ................................................ 30
   3.3  Four-vectors and -tensors .............................. 31
   3.4  Manifest covariance of the free Maxwell equations ...... 33
   3.5  Lorentz transformation of the (transverse) electric
        and magnetic fields. Duality ........................... 35
   3.6  Lorentz transformation of Riemann-Silberstein
        vectors. Inner-product invariance ...................... 38

II Light rays and geodesies. Maxwell theory in general
   relativity .................................................. 39
4  The light-particle and wave pictures in classical physics ... 41
5  Eikonal theory and Fermat's principle ....................... 45
   5.1  Remarks on geometrical optics. Inhomogeneous vacuum .... 45
   5.2  Eikonal equation. Geometrical wave surfaces and rays ... 47
   5.3  Geodetic line: Fermat's principle ...................... 52
6  Geodesies in general relativity ............................. 55
   6.1  Metric tensor. Four-dimensional Riemann space .......... 55
   6.2  Time-like metric geodesies ............................. 56
   6.3  The Newtonian limit: Motion in a weak static
        gravitational field .................................... 59
   6.4  Null geodesies and "light particles" ................... 61
   6.5  Gravitational redshift. Photon in free fall ............ 62
7  The space-time of general relativity ........................ 67
   7.1  Tensor fields .......................................... 67
   7.2  Covariant derivative ................................... 69
   7.3  Parallel transport ..................................... 70
   7.4  Riemann curvature tensor ............................... 71
   7.5  Algebraic properties of the Riemann curvature tensor ... 73
   7.6  Einstein field equations in general relativity ......... 74
   7.7  Metric compatibility ................................... 76
   7.8  Geodesic deviation of light rays ....................... 76
8  Electromagnetic theory in curved space-time ................. 79
   8.1  Vacuum Maxwell equations in general relativity ......... 79
   8.2  Covariant curl and divergence in Riemann space ......... 80
   8.3  A uniform formulation of electrodynamics in curved
        and fiat space-time .................................... 81
        8.3.1  Maxwell equations with normal derivatives ....... 81
        8.3.2  Maxwell equations with E, B, D, and H fields .... 83
        8.3.3  Microscopic Maxwell-Lorentz equations in
               curved space-time ............................... 84
        8.3.4  Constitutive relations in curved space-time ..... 85
        8.3.5  Remarks on the constitutive relations in
               Minkowskian space ............................... 87
        8.3.6  Permittivity and permeability for static
               metrics ......................................... 88
   8.4  Permittivity and permeability in expanding universe .... 89
   8.5  Electrodynamics in potential description. Eikonal
        theory and null geodesies .............................. 91
   8.6  Gauge-covariant derivative ............................. 95

III Photon wave mechanics ...................................... 97
9  The elusive light particle .................................. 99
10 Wave mechanics based on transverse vector potential ........ 105
   10.1 Gauge transformation. Covariant and noncovariant
        gauges ................................................ 105
   10.2 Tentative wave function and wave equation for
        transverse photons .................................... 107
   10.3 Transverse photon as a spin-1 particle ................ 110
   10.4 Neutrino wave mechanics. Massive eigenstate
        neutrinos ............................................. 113
11 Longitudinal and scalar photons. Gauge and near-field
   light quanta ............................................... 119
   11.1 L- and S-photons. Wave equations ...................... 119
   11.2 L- and S-photon neutralization in free space .......... 120
   11.3 NF- and G-photons ..................................... 122
   11.4 Gauge transformation within the Lorenz gauge .......... 124
12 Massive photon field ....................................... 127
   12.1 Proca equation ........................................ 127
   12.2 Dynamical equations for E and A ....................... 129
   12.3 Diamagnetic interaction: Transverse photon mass ....... 130
   12.4 Massive vector boson (photon) field ................... 132
   12.5 Massive photon propagator ............................. 136
13 Photon-energy wave function formalism ...................... 143
   13.1 The Oppenheimer light quantum theory .................. 143
   13.2 Interlude: From spherical to Cartesian
        representation ........................................ 146
   13.3 Photons and antiphotons: Bispinor wave functions ...... 150
   13.4 Four-momentum and spin of photon wave packet .......... 153
   13.5 Relativistic scalar product. Lorentz-invariant
        integration on the energy shell ....................... 155

IV  Single-photon quantum optics in Minkowskian space ......... 159
14 The photon of the quantized electromagnetic field .......... 161
15 Polychromatic photons ...................................... 165
   15.1 Canonical quantization of the transverse
        electromagnetic field ................................. 165
   15.2 Energy, momentum, and spin operators of the
        transverse field ...................................... 168
   15.3 Monochromatic plane-wave photons. Fock states ......... 171
   15.4 Single-photon wave packets ............................ 173
   15.5 New T-photon "mean" position state .................... 177
   15.6 T-photon wave function and related dynamical
        equation .............................................. 179
   15.7 The non-orthogonality of T-photon position states ..... 181
16 Single-photon wave packet correlations ..................... 183
   16.1 Wave-packet basis for one-photon states ............... 183
   16.2 Wave-packet photons related to a given i-matrix ....... 184
   16.3 Integral equation for the time evolution operator in
        the interaction picture ............................... 186
   16.4 Atomic and field correlation matrices ................. 189
   16.5 Single-photon correlation matrix: The wave function
        fingerprint ........................................... 194
17 Interference phenomena with single-photon states ........... 197
   17.1 Wave-packet mode interference ......................... 197
   17.2 Young-type double-source interference ................. 198
   17.3 Interference between transition amplitudes ............ 201
   17.4 Field correlations in photon mean position state ...... 201
        17.4.1 Correlation supermatrix ........................ 202
        17.4.2 Relation between the correlation supermatrix
               and the transverse photon propagator ........... 203
18 Free-field operators: Time evolution and commutation
   relations .................................................. 205
   18.1 Maxwell operator equations. Quasi-classical states .... 205
   18.2 Generalized Landau-Peierls-Sudarshan equations ........ 207
   18.3 Commutation relations ................................. 208
        18.3.1 Commutation relations at different times
               (τ≠0) .......................................... 209
        18.3.2 Equal-time commutation relations ............... 210

V  Photon embryo states ....................................... 213
19 Attached photons in rim zones .............................. 215
20 Evanescent photon fields ................................... 221
   20.1 Four-potential description in the Lorenz gauge ........ 221
   20.2 Sheet current density: T-, L-, and S-parts ............ 223
   20.3 Evanescent T-, L-, and S-potentials ................... 225
   20.4 Four-potential photon wave mechanics .................. 229
   20.5 Field-quantized approach .............................. 231
   20.6 Near-field photon: Heisenberg equation of motion and
        coherent state ........................................ 234
21 Photon tunneling ........................................... 237
   21.1 Near-field interaction. The photon measurement
        problem ............................................... 237
   21.2 Scattering of a wave-packet band from a single
        current-density sheet ................................. 238
   21.3 Incident fields generating evanescent tunneling
        potentials ............................................ 243
   21.4 Interlude: Scalar propagator in various domains ....... 246
   21.5 Incident polychromatic single-photon state ............ 247
   21.6 Photon tunneling-coupled sheets ....................... 250
22 Near-field photon emission in 3D ........................... 255
   22.1 T-, L-, and S-potentials of a classical point-
        particle .............................................. 255
        22.1.1 General considerations on source fields ........ 255
        22.1.2 Point-particle potentials ...................... 257
   22.2 Cerenkov shock wave ................................... 260
        22.2.1 Four-potential of point-particle in uniform
               motion in vacuum ............................... 260
        22.2.2 Transverse and longitudinal response theory
               in matter ...................................... 263
        22.2.3 The transverse Cerenkov phenomenon ............. 266
        22.2.4 Momenta associated to the transverse and
               longitudinal parts of the Cerenkov field ....... 269
        22.2.5 Screened canonical particle momentum ........... 272

VI Photon source domain and propagators ....................... 275

23 Super-confined T-photon sources ............................ 277
24 Transverse current density in nonrelativistic quantum
   mechanics .................................................. 283
   24.1 Single-particle transition current density ............ 283
   24.2 The hydrogen 1s  2pz transition ...................... 286
   24.3 Breathing mode: Hydrogen 1s  2pz transition .......... 289
   24.4 Two-level breathing mode dynamics ..................... 292
25 Spin-1/2 current density in relativistic quantum
   mechanics .................................................. 297
   25.1 Dirac matrices ........................................ 297
   25.2 Covariant form of the Dirac equation. Minimal
        coupling. Four-current density ........................ 299
   25.3 Gordon decomposition of the Dirac four-current
        density ............................................... 301
   25.4 Weakly relativistic spin current density .............. 303
   25.5 Continuity equations for spin and space four-current
        densities ............................................. 306
26 Massless photon propagators ................................ 309
   26.1 From the Huygens propagator to the transverse photon
        propagator ............................................ 309
   26.2 T-photon time-ordered correlation of events ........... 311
   26.3 Covariant correlation matrix .......................... 313
   26.4 Covariant quantization of the electromagnetic field:
        A brief review ........................................ 314
   26.5 The Feynman photon propagator ......................... 316
   26.6 Longitudinal and scalar photon propagators ............ 318

VII Photon vacuum and quanta in Minkowskian space ............. 321
27 Photons and observers ...................................... 323
28 The inertial class of observers: Photon vacuum and quanta .. 329
   28.1 Transverse photon four-current density ................ 329
   28.2 Boosts ................................................ 332
        28.2.1 Lorentz and Lorenz-gauge transformations of
               the four-potential ............................. 332
        28.2.2 Plane-mode decomposition of the covariant
               potential ...................................... 333
        28.2.3 Mode functions ................................. 336
   28.3 Physical (T-photon) vacuum ............................ 337
29 The non-inertial class of observers: The nebulous
   particle concept ........................................... 345
   29.1 Bogolubov transformation. Vacuum states ............... 345
   29.2 The non-unique vacuum ................................. 348
   29.3 The Unruh effect ...................................... 352
        29.3.1 Rindler space and observer ..................... 352
        29.3.2 Rindler particles in Minkowski vacuum .......... 354
30 Photon mass and hidden gauge invariance .................... 363
   30.1 Physical vacuum: Spontaneous symmetry breaking ........ 363
   30.2 Goldstone bosons ...................................... 366
   30.3 The U(1) Higgs model .................................. 368
   30.4 Photon mass and vacuum screening current .............. 372
   30.5 't Hooft gauge and propagator ......................... 373

VIII Two-photon entanglement in space-time .................... 377
31 The quantal photon gas ..................................... 379
32 Quantum measurements ....................................... 385
   32.1 Tensor product space (discrete case) .................. 385
   32.2 Definition of an observable (discrete case) ........... 386
   32.3 Reduction of the wave packet (discrete case) .......... 387
   32.4 Measurements on only one part of a two-part physical
        system ................................................ 387
   32.5 Entangled photon polarization states .................. 390
33 Two-photon wave mechanics and correlation matrices ......... 393
   33.1 Two-photon two times wave function .................... 393
   33.2 Two-photon Schrödinger equation in direct space ....... 396
   33.3 Two-photon wave packet correlations ................... 397
        33.3.1 First-order correlation matrix ................. 397
        33.3.2 Second-order correlation matrix ................ 399
34 Spontaneous one- and two-photon emissions .................. 401
   34.1 Two-level atom: Weisskopf-Wigner theory of
        spontaneous emission .................................. 401
        34.1.1 Atom-field Hamiltonian in the electric-dipole
               approximation. RWA-model ....................... 401
        34.1.2 Weisskopf-Wigner state vector .................. 406
   34.2 Two-level atom: Wave function of spontaneously
        emitted photon ........................................ 409
        34.2.1 Photon wave function in q-space ................ 409
        34.2.2 The general photon wave function in r-space .... 410
        34.2.3 Genuine transverse photon wave function ........ 411
        34.2.4 Spontaneous photon emission in the atomic rim
               zone ........................................... 413
   34.3 Three-level atom: Spontaneous cascade emission ........ 417
        34.3.1 Two-photon state vector ........................ 417
        34.3.2 Two-photon two-times wave function ............. 420
        34.3.3 The structure of Ф2,T(r1,r2,t1,t2) ............... 422
        34.3.4 Far-field part of Ф(1)2,T(r1,r2,t1,t2) ............ 425
Bibliography .................................................. 429
Index ......................................................... 441

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