Simon B. — Functional Integration and Quantum Physics :: Электронная библиотека попечительского совета мехмата МГУ

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Simon B. — Functional Integration and Quantum Physics

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Название: Functional Integration and Quantum Physics

Автор: Simon B.

Аннотация:

This work makes path integrals available as a tool to practicing mathematical physicists, and will open up new areas of research to probabilists. Coverage progresses from basic processes through bound state problems, inequalities, magnetic fields and stochastic integrals, and asymptotics. Simon has lectured in physics at the University of Geneva, Switzerland. This second edition includes brief bibliographic notes reflecting developments taking place in the field over the past 30 years.

Язык:

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 296

Добавлена в каталог: 01.10.2005

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Предметный указатель

$P(\phi)_1$ process      57
Abelian theorem (Th. 10.2)      107
Anharmonic oscillator      2 124 135 139 146 183 186 211—224
Arcsin law (Th. 6.10)      58—60
Asymptotic series      212
Bender — Wu formula (Eq. (18.8))      184
Birkhoff ergodic theorem      see Ergodic theorem
Birman — Kato theorem (Th. 21.2)      227
Birman — Schwinger principle (Th. 8.1)      89
Borel — Cantelli lemmas (Ths. 3.1, 3.2)      18
Born — Oppenheimer Hamiltonian      3 123 141
Brownian bridge      40
Brownian motion      33
Brownian motion $\nu$ -dimensional      36
Brownian motion, conditional      40
Brunn — Minkowski inequality (Th. 13.7)      139—141
Cameron — Martin formula      172
Capacity      84—87
Carmona’s estimate (Th. 25.11)      267
Cartier’s formula (Eq. (12.16))      131
Central limit theorem (Th. 4.1)      32
Characteristic function of a random variable      10
Classical limits      see Semiclassical limit
Completeness of wave operators      226
Conditional expectation      21
Conditional measure      68
Conditioning      145
Consistent probability distributions      8
Convergence in probability      235
Convergence of measures, weak      175
Convex function      93
Correlation functions      246
Cumulants      see Ursell functions
Cwickel — Lieb — Rosenbljum bound (Th. 9.3)      95—96
Cylinder sets      10 12
De Moivre — Laplace limit theorem      32
Diamagnetic inequality (Eqs. (1.1), (15.9), (15.10))      2 163—164
Dirichlet Green's function methods      69—73
Dirichlet Laplacian      69 224
Donsker — Varadhan theory      198—210
Donsker’s theorem (Th. 17.1)      176
Doob’s inequality (Th. 3.5)      23
Double points      see n-fold points
Drift process      172
Dynkin — Hunt theorem (Th. 7.9)      68
Eigenfunction, properties of, Schroedinger      264—272
Elementary random walk      32
Entropy per unit volume      200—201
Erdoes — Kac invariance principle      175
Ergodic map      25—26
Ergodic theorem (Th. 3.7)      26
Euclidean Green’s function      224
Event      8
Existence of wave operators      226
Feldman — Hajek theorem (Th. 2.5)      17 189
Feynman diagram      218
Feynman graph,      218
Feynman path integral      6—7
Feynman — Kac formula (Eq. (6.1))      48—53 156
Feynman — Kac — Ito formula (Eqs. (15.1), (15.2))      159—163 171
Feynman’s inequality      see Jensen's inequality
FKG inequality      126
Free Euclidean field      256
Friedman’s theorem      72
Froelich's reconstruction theorem (Th. 24.1)      254
Gauge invariance      160—161
Gaussian inequality      see Newman's inequality
Gaussian Markov processes      41—42
Gaussian process      16
Gaussian random variable      15 27—31
Gaussian, jointly      15 16
Gaussian, variance of      15
Generalized positive operator      5
GHS inequality      129—134
Gibbs’ principle      201
Gibbs’ variational inequality      201
GKS inequality      120—123
Golden — Thompson inequality (Th. 9.2)      94
Grand canonical partition function      246
Green’s function, properties of Schroedinger      262
Harmonic function methods      82—87
Hitting probabilities      70—72 82—84
Hoelder continuous paths (Th. 5.2)      45
Hypercontractive estimates (Th. 13.14)      146
Independent random variables      21
Independent, identically distribultted      19
Individual ergodic theorem      see Ergodic theorem
Inequalities      see specific inequalities
Iterated logarithm, law of (Ths. 7.1-7.5)      60—64
Ito integral      153
Ito’s lemma (Ths. 14.3, 16.1)      153 170
Jensen’s inequality (Prop. 9.1)      93
Khintchine’s law      see Iterated logarithm

Kolmogorov’s 01 law      26
Kolmogorov’s lemma (Th. 5.1)      43-44
Kolmogorov’s theorem (Th. 2.1)      9
Labeled graph      218
Laplace’s method      181
Law of large numbers, strong (Lemma 7.14)      75
Law of the iterated logarithm      60—64
Lebowitz inequality      129 131
Levy’s local modulus law (Th. 5.3)      45
Levy’s maximal inequality (Th. 3.6.5)      25
Lieb — Thirrng bound (Eq. (9.25))      100
Lieb’s formula (Th. 8.2)      90
Local time      208
Log concave functions      136
Loop momenta      223
Magnetic fields      2 3 127—128 159—170
Markov(ian) processes      41—43
Martingale      22—24
Mehler’s formula      27 38 55
Method of images      70
Minlos’ theorem (Ths. 2.2, 2.3)      11—13
Model      10
n-fold points of Brownian motion      81—87
Newman’s inequality      129
Newtonian capacity      84—87
Nonanticipatory functional      153
Nondifferentiability of paths (Th. 5.4)      46
Ornstein — Uhlenbeck velocity process      35
Oscillator process      34
Park’s correlation inequality (Th. 23.4a)      250
Path’s properties of arcsinlaw      58—60
Path’s properties of hitting probabilities      70—72 82—84
Path’s properties of Hoelder continuity      45
Path’s properties of iterated logarithm      60—64
Path’s properties of n-fold points      81—87
Path’s properties of nondifferentiability      46
Path’s properties of nonrectifiable      148
Path’s properties of recurrence      73—81
Path’s properties of Wiener sausage      236
Path’s properties of zeros of      61
Percus’ lemma (Prop. 12.11)      130
Portenko’s lemma (Th. 11.2)      117
Positive definite      10
Pressure      200—201 246
Probability distribution, joint      8
Probability distributions of Brownian motion $E(\inf\{s|b(s)=1\}\ge s_0)$       76—79
Probability distributions of Brownian motion $E(\max\limits_{0\le s\le t} b(s)\ge \lambda)$       64—67 76
Probability distributions of Brownian motion $E(|(R, 0,\ldots, 0)+ b(s)|\le r; \mathrm{some\ } s)$       70—72 83—84
Probability distributions of Brownian motion $E(|\{s\le1|b(s)\ge0\}|)$       59—60
Probability measure space      8
Prohorov’s theorem (Th. 17.4)      177
Quasi-classical limit      see Semiclassical limit
Random variable      8
Recurrence properties of Brownian motion      73—81
Reflection principle      25 64
Regular set      69
Schwinger functions      253
Self-intersection      see n-fold points of
Semiclassical limit      1 7 105—114 164—167 195—198
Shale’s theorem (Th. 2.5)      17 189
Sine — Gordon transformation      249
Stability of matter (Ths. 9.6, 15.12)      98—105 168
Statistical mechanical analog      58 198
Stochastic integral      170
Stochastic process      13
Stopping time      65
Stopping time, discretization of      66
Strong Law of Large Numbers      75
Submartinaggale      22—24
Symanzik’s inequality (Th. 9.2)      94
Symmetric decreasing function      142
Symmetric decreasing rearrangement      143
Symmetry numbers      219
Tauberian theorem (Th. 10.3)      108
Teller’s lemma (Lemma 9.10)      105
Teller’s theorem (Th. 9.11)      105
Thomas — Fermi theory      98 102—105
Tight family of measures      177
Trotter product formula (Th. 1.1)      4—6
Uniformly distributed of degree m      233
Uniformly locally       260
Unlabeled graph      219
Ursell functions      129
Versions      13—14 44
Wave operators      226
Weak convergence of measures      175
Weak coupling      114—118
Weiner measure      38
Weiner measure, conditional      39
Wick ordered exponential      28 155
Wick’s theorem (Lemma 20.4)      217
Wiener process      33
Wiener sausage      209

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