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Simon B. Ч Functional Integration and Quantum Physics
Simon B. Ч Functional Integration and Quantum Physics

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Ќазвание: Functional Integration and Quantum Physics

јвтор: Simon B.

јннотаци€:

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: en

–убрика: ‘изика/ вантова€ теори€ пол€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1979

 оличество страниц: 296

ƒобавлена в каталог: 01.10.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$P(\phi)_1$ process      57
Abelian theorem (Th. 10.2)      107
Anharmonic oscillator      2 124 135 139 146 183 186 211Ч224
Arcsin law (Th. 6.10)      58Ч60
Asymptotic series      212
Bender Ч Wu formula (Eq. (18.8))      184
Birkhoff ergodic theorem      see Ergodic theorem
Birman Ч Kato theorem (Th. 21.2)      227
Birman Ч Schwinger principle (Th. 8.1)      89
Borel Ч Cantelli lemmas (Ths. 3.1, 3.2)      18
Born Ч Oppenheimer Hamiltonian      3 123 141
Brownian bridge      40
Brownian motion      33
Brownian motion $\nu$-dimensional      36
Brownian motion, conditional      40
Brunn Ч Minkowski inequality (Th. 13.7)      139Ч141
Cameron Ч Martin formula      172
Capacity      84Ч87
CarmonaТs estimate (Th. 25.11)      267
CartierТs 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 Ч Lieb Ч Rosenbljum bound (Th. 9.3)      95Ч96
Cylinder sets      10 12
De Moivre Ч Laplace limit theorem      32
Diamagnetic inequality (Eqs. (1.1), (15.9), (15.10))      2 163Ч164
Dirichlet Green's function methods      69Ч73
Dirichlet Laplacian      69 224
Donsker Ч Varadhan theory      198Ч210
DonskerТs theorem (Th. 17.1)      176
DoobТs inequality (Th. 3.5)      23
Double points      see n-fold points
Drift process      172
Dynkin Ч Hunt theorem (Th. 7.9)      68
Eigenfunction, properties of, Schroedinger      264Ч272
Elementary random walk      32
Entropy per unit volume      200Ч201
Erdoes Ч Kac invariance principle      175
Ergodic map      25Ч26
Ergodic theorem (Th. 3.7)      26
Euclidean GreenТs function      224
Event      8
Existence of wave operators      226
Feldman Ч Hajek theorem (Th. 2.5)      17 189
Feynman diagram      218
Feynman graph,      218
Feynman path integral      6Ч7
Feynman Ч Kac formula (Eq. (6.1))      48Ч53 156
Feynman Ч Kac Ч Ito formula (Eqs. (15.1), (15.2))      159Ч163 171
FeynmanТs inequality      see Jensen's inequality
FKG inequality      126
Free Euclidean field      256
FriedmanТs theorem      72
Froelich's reconstruction theorem (Th. 24.1)      254
Gauge invariance      160Ч161
Gaussian inequality      see Newman's inequality
Gaussian Markov processes      41Ч42
Gaussian process      16
Gaussian random variable      15 27Ч31
Gaussian, jointly      15 16
Gaussian, variance of      15
Generalized positive operator      5
GHS inequality      129Ч134
GibbsТ principle      201
GibbsТ variational inequality      201
GKS inequality      120Ч123
Golden Ч Thompson inequality (Th. 9.2)      94
Grand canonical partition function      246
GreenТs function, properties of Schroedinger      262
Harmonic function methods      82Ч87
Hitting probabilities      70Ч72 82Ч84
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)      60Ч64
Ito integral      153
ItoТs lemma (Ths. 14.3, 16.1)      153 170
JensenТs inequality (Prop. 9.1)      93
KhintchineТs law      see Iterated logarithm
KolmogorovТs 01 law      26
KolmogorovТs lemma (Th. 5.1)      43-44
KolmogorovТs theorem (Th. 2.1)      9
Labeled graph      218
LaplaceТs method      181
Law of large numbers, strong (Lemma 7.14)      75
Law of the iterated logarithm      60Ч64
Lebowitz inequality      129 131
LevyТs local modulus law (Th. 5.3)      45
LevyТs maximal inequality (Th. 3.6.5)      25
Lieb Ч Thirrng bound (Eq. (9.25))      100
LiebТs formula (Th. 8.2)      90
Local time      208
Log concave functions      136
Loop momenta      223
Magnetic fields      2 3 127Ч128 159Ч170
Markov(ian) processes      41Ч43
Martingale      22Ч24
MehlerТs formula      27 38 55
Method of images      70
MinlosТ theorem (Ths. 2.2, 2.3)      11Ч13
Model      10
n-fold points of Brownian motion      81Ч87
NewmanТs inequality      129
Newtonian capacity      84Ч87
Nonanticipatory functional      153
Nondifferentiability of paths (Th. 5.4)      46
Ornstein Ч Uhlenbeck velocity process      35
Oscillator process      34
ParkТs correlation inequality (Th. 23.4a)      250
PathТs properties of arcsinlaw      58Ч60
PathТs properties of hitting probabilities      70Ч72 82Ч84
PathТs properties of Hoelder continuity      45
PathТs properties of iterated logarithm      60Ч64
PathТs properties of n-fold points      81Ч87
PathТs properties of nondifferentiability      46
PathТs properties of nonrectifiable      148
PathТs properties of recurrence      73Ч81
PathТs properties of Wiener sausage      236
PathТs properties of zeros of      61
PercusТ lemma (Prop. 12.11)      130
PortenkoТs lemma (Th. 11.2)      117
Positive definite      10
Pressure      200Ч201 246
Probability distribution, joint      8
Probability distributions of Brownian motion $E(\inf\{s|b(s)=1\}\ge s_0)$      76Ч79
Probability distributions of Brownian motion $E(\max\limits_{0\le s\le t} b(s)\ge \lambda)$      64Ч67 76
Probability distributions of Brownian motion $E(|(R, 0,\ldots, 0)+ b(s)|\le r; \mathrm{some\ } s)$      70Ч72 83Ч84
Probability distributions of Brownian motion $E(|\{s\le1|b(s)\ge0\}|)$      59Ч60
Probability measure space      8
ProhorovТs theorem (Th. 17.4)      177
Quasi-classical limit      see Semiclassical limit
Random variable      8
Recurrence properties of Brownian motion      73Ч81
Reflection principle      25 64
Regular set      69
Schwinger functions      253
Self-intersection      see n-fold points of
Semiclassical limit      1 7 105Ч114 164Ч167 195Ч198
ShaleТs theorem (Th. 2.5)      17 189
Sine Ч Gordon transformation      249
Stability of matter (Ths. 9.6, 15.12)      98Ч105 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      22Ч24
SymanzikТs inequality (Th. 9.2)      94
Symmetric decreasing function      142
Symmetric decreasing rearrangement      143
Symmetry numbers      219
Tauberian theorem (Th. 10.3)      108
TellerТs lemma (Lemma 9.10)      105
TellerТs theorem (Th. 9.11)      105
Thomas Ч Fermi theory      98 102Ч105
Tight family of measures      177
Trotter product formula (Th. 1.1)      4Ч6
Uniformly distributed of degree m      233
Uniformly locally $L^p$      260
Unlabeled graph      219
Ursell functions      129
Versions      13Ч14 44
Wave operators      226
Weak convergence of measures      175
Weak coupling      114Ч118
Weiner measure      38
Weiner measure, conditional      39
Wick ordered exponential      28 155
WickТs theorem (Lemma 20.4)      217
Wiener process      33
Wiener sausage      209
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