Kaiser G. — Quantum physics, relativity, and complex spacetime: Towards a new synthesis :: Электронная библиотека попечительского совета мехмата МГУ

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Kaiser G. — Quantum physics, relativity, and complex spacetime: Towards a new synthesis

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Название: Quantum physics, relativity, and complex spacetime: Towards a new synthesis

Автор: Kaiser G.

Аннотация:

A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 376

Добавлена в каталог: 24.03.2014

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Предметный указатель

Admissible      49 100 112 339
Affine group      46
Analytic signal      239
Analytic vector      116
Analytic-signal transform      243ff 335 343
Anticommutators      292
Averaging operator h(S)      62ff 75
Bosons      293
Bra-ket notation      6ff
Canonical anticommutation relations      294
Canonical commutation relations      9 11 162 276
Canonical transformation      211
Cartan subalgebra      117
Central extension      168
Characteristic function      312
Charge      264ff 282 296
Charge current $j^{\mu}$       284 296
Charge, density $\rho$       283 296
Coherent state representation      13ff
Coherent state, canonical      9ff 115
Coherent state, Galilean $e^{u}_{x}$       172ff
Coherent state, holomorphic      130
Coherent state, interpolating      302ff
Coherent state, relativistic $e_{z}$       190ff
Complex line bundle      323
Complex manifold      129
Complex structure J      70ff
Complex vector bundle      328
Configuration space S      208 212
Conjugation operator C      72
Connection      322ff
Connection form      324
Connection, Riemannian      323
Connection, type (1, 0)      333
Consistency condition      22 340
Contraction limit      121 145ff 161
Control vector y      195 272
Coset spaces      109
Covariant derivative $D_{X}$       324ff
Curvature $\Theta$       331
De Broglie's relation      4
Decomposition      82ff
Decomposition, complex      87ff
Differencing operator g(S)      75
Dilation      45 58 336
Dilation equation      63
Dilation operator D      62
Dirac equation      393
Dirac equation field $\psi$       289ff
Directional holomorphy      247
Electromagnetic field F      326
Electromagnetic potential A      325
Energy      4
Evaluation maps      32 190
Exponential step function $\theta^{\zeta}$       241
fermions      293
Fiber      323
Fiber metric h      325 329
Field coherent state      308ff
Filter, bandpass      45
Filter, complex Z, $\tilde{Z}$       85ff
Filter, high-pass $G_{\alpha}$       78ff
Filter, low-pass $H_{\alpha}$       65
Fourier transform      3 5
Fourier transform, windowed      34 36
Fourier — Laplace transform      240 244 344
Frame      18ff 33 37 49
Frame bundle      159
Frame, discrete      38—40 55
Functional integral      316
Galilean group $\mathcal{G}$       163ff
Gauge group      327
Gauge symmetry      300
Gauge transformation      324
General relativity      321
Gordon identity      297
Group frame      95ff
Group frame, holomorphic      113ff
Group frame, homogeneous      103ff
Haar basis      63 75
harmonic oscillator      11 145ff
Heisenberg algebra      9
Heisenberg picture      198
Hilbert transform $H_{y}$       247 345
Hilbert transform H      243

Holomorphic gauge transformation      329
Home space V      65
Home versions      65
Homogeneous space      110
Interpolation operator $H^{\ast}_{\alpha}$       65
Killing form      119
Klein — Gordon equation      185ff
Klein — Gordon field $\phi$       273ff
Light cones $V_{+}, V^{'}_{+}$       189
Lorentz group $\mathcal{L}$       157
Lorentz metric      2
Lorentzian spacetime      2
Mass m      162
Mass shell $\Omega_{m}$       185
Metric      322ff
Minimal coupling      326
Moebius transformation      140
Momentum      4
Multiscale analysis      58 64
Natural units      5
Naturality      65
Non-relativistic limit      225ff
Number operators $N_{\pm}$       281 295
Orientation      213
Oversampling      41
Particle coherent state      266
Pauli exclusion principle      293
Phase space      36 156
Phase space, $\sigma$       202 207ff 279ff
Planck's Ansatz      4
Poincare group $\mathcal{P}$       157ff
Polarization (of frequencies)      301
Position operators      162 198
Probability current      207ff 215 219
Probability density, relativistic      206
Quantization      162—163
Radon transform      342
Reconstruction      38 40 82ff 336ff
Reconstruction, complex      87ff
Regularized current      285 298
Representation of group      33 96 124
Representation of vector space      8
Representation, projective      112
Representation, Schroedinger      9 105
Representation, square-integrable      49 112
Reproducing kernel      22 29ff 49 193 287 298
Resolution of unity      8 15 18ff 23 24 37 49 205ff
Root      118
Root subspace      118
Root vector      118
Sampling rate      50
Sampling, time-frequency      40
Schroedinger equation      169
Section (of bundle)      109
Shift operator S      60
signal      34
Spin coherent state      135
State space $\mathcal{C}$       159
Statistics      293
Stereographic projection      145
Symplectic form      135 208ff
Symplectic geometry      155
Temper vector      197 272
Tube $\mathcal{T}$       190 249
Two-point functions $\Delta^{\pm}$       193 268 287
Uncertainty principle      5 10 163
Vector bundle      328
Vector potential $A_{mu}$       326
Wave number vector      4
Wavelet      44
Wavelet transform      44ff 334ff
Wavelet, mother (basic) $\psi$       44 58 75 79
Weight      126
Weyl — Heisenberg, group $\mathcal{W}$       38 104 159ff
Wick ordering      282ff
Wightman axioms      252ff
Window      35
Window, relativistic      58 178 334
X-ray transform      245 341
X-ray transform, windowed      334ff
Yang — Mills field      331—332
Yang — Mills field potential      331
Yang — Mills field theory      327
Zitterbewegung      301
Zoom operators H, H*      66 84

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