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Reed M., Simon B. — Methods of Modern mathematical physics (vol. 2) Fourier analysis, self-adjointness
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Название: Methods of Modern mathematical physics (vol. 2) Fourier analysis, self-adjointnessАвторы: Reed M., Simon B. Аннотация: This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.
Язык: Рубрика: Математика /Математическая Физика /Учебники /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1975Количество страниц: 370Добавлена в каталог: 24.04.2005Операции: Положить на полку |
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201 32 255 A-bounded 162 A-closed 138 A-compact 340 A-orthogonal 138 A-symmetric 138 Absolute value of an operator 196 Absolutely continuous subspace 230 Accretive operator 240 action 275 Adjoint, Banach space 185 Adjoint, Hilbert space 186 Adjoint, unbounded operator 252 Almost completeness 338 Analytic Fredholm theorem 201 Analytic function, vector-valued 189—190 Analytic vector 201 Anharmonic oscillator 17 184 206 266 270 Annihilation operator 142 208 217 218 219 Antilinear operator 69 Approximate identity 251 9 Approximate symbol 98 Ascoli’s Theorem 30 Asymptotic symbol 98 Atomic model 304 Axiomatic quantum field theory 62 B.L.T. theorem 9 Baire category theorem 80 Baire measure 105 110 Banach — Alaoglu theorem 115 Bessel’s inequality 38 Bochner integral 119 Bochner — Schwartz theorem 14 Bochner’s theorem 13 Boson Fock space 53 Boundary value 19 Bounded holomorphic semigroup 248 Bounded operator 8 Bros — Epstein — Glaser lemma 21 Canonical commutation relations 274 218 232 Canonical conjugate momentum 215 Canonical form for compact operators 203 Canonical free field 215 Cauchy principal value 136 Closable operator 250 252—253 Closed graph theorem 83 Closed operator 250 Closed quadratic form 277 Closure 92 Closure of an operator 250 Commuting (unbounded) operators 271—272 Compact operator 199 Compact support, distributions 139 178 17 Compact support, functions 111 Complete, classically 148 Complete, quantum mechanically 155 Completely continuous operator (see “Compact operator”) Cone 109 19 Cone, dual 19 Conjugation 143 Consistent norms 35 Continuous functional calculus 222 Contraction mapping theorem 151 Contraction mapping theorem, semigroup 235 Convex cone 109 Convex set 109 Convolution distributions 7 Convolution distributions, functions 6 Core 256 Coulomb gauge condition 190 Creation operator 142 204 209 217—219 Cyclic vector 226 Cyclicity of the vacuum 65 Davies — Faris theorem 186 Deficiency indices 138 Deficiency subspace 138 Densely bounded 272 Dirac operator 326 337 Distributions compact support 139 178 17 Domain 2 Dominated Convergence Theorem 17 24 Dual cone 19 Dunford functional calculus 245 Dunford — Taylor formula 316 Dyson expansion 282E Elliptic operator 112 Elliptic regularity 49 Energy operator (see “Hamiltonian”) Equivalent representations 231 Essential range 229 Essentially self-adjoint 256 Extended forward tube 68 Extension of an operator 250 Faris — Lavine theorem 199 Fermion Fock space 54 Feynman — Kac formula 279 Finite particle vector 208 Finite propagation speed 309—310 First resolvent formula 191 Fock space 53 Form core 277 Form domain 276 Form domain of operator 277 Forward 66 Forward tube 66 Fourier inversion theorem 3 Fourier transform 1 Frechet space 132 Free field 212 215 217 223 Free Green’s function 59 Free Hamiltonian mass m (quantum field theory) 220 Free propagator 60 Friedrichs extension 177 Functional calculus 222 225 245 263 286—287 Functions of rapid decrease 133 Fundamental solution 46 Garding — Wightman axioms 61—65 Gauge condition 190 Generalized convergence (see “Norm resolvent sense” “Strong Generalized function 148 Generator group 268 Generator group, semigroup 237 246 Graph 83 250 Graph limits 293—294 268 Green’s functions 59 Hadamard’s three line theorem 33 Hahn — Banach theorem 75—77 130 Hamburger moment problem existence 145 Hamburger moment problem existence, uniqueness 205 Hamiltonian 303 Hamiltonian, free 55 220 Hamiltonian, time dependent 109 Hardy — Lebesgue class 109 Hausdorff — Young inequality 11 Heat equation 242 243 245 254 Hermite functions 142 Hermite functions, completeness 121 Hermitian operator (see “Symmetric operator”) Hermitian scalar quantum field theory 62 212 Hilbert — Schmidt operators 210—211 Hilbert — Schmidt theorem 203 Hille — Yosida theorem 238 Hille — Yosida — Phillips theorem 247 Hoelder continuous 81 Hoelder inequality 68 34 Holomorphic semigroup 252 Holomorphic semigroup, bounded 248 Hunt's interpolation theorem 31 Hypercontractive semigroup 258 Hypersurface 78 Hypoelliptic 112 Inequalities 32 Infinitesimal generator, group 268 Infinitesimal generator, semigroup 237 246 Infinitesimally small form 168 Infinitesimally small operator 162 Interaction representation 283 Interpolation, norms 37 Interpolation, spaces 37 Interpolation, theorem, Calder — Lions 37 Interpolation, theorem, Hunt 31 Interpolation, theorem, Marcinkievvicz 31 Interpolation, theorem, Stein 40 Inverse Fourier transform 1 Irreducible 232 Jost points 68 Kalf — Walter — Schmincke — Simon theorem 186 Kallen — Lehmann representation 70 Kato — Rellich theorem 162 Kato — Rellich theorem, symmetric form 163 Kato’s inequality 183 Kato’s theorem 166 Klein — Gordon equation 293 KLMN theorem 167 Konrady’s trick 175 Light cone 63 Limit circle 1 Limit point 1 Liouville form 314 Liouville operator 314 Liouville’s theorem 315 Lipschitz 154 Local commutativity 65 Local Sobolev space 51 Lorentz group 63 Lorentz invariant inner product 63 Lorentz invariant inner product, measures 74 m-accretive 168 240 Magnetic field 173 Magnetic vector potential 173 Malgrange — Ehrenpreis theorem 48 Manifold stationary phase 101 Manifold stationary phase, Symplectic 337 Marcinkiewicz interpolation theorem 31 Mass hyperboloids 70 Mathieu equation 320 Maximal accretive operator 240 Maximal interval of existence 301 Maximal symmetric operator 141 Microscopic causality 65 Moments of a measure 145 Momentum operators 304 65 Monotone Convergence Theorem 17 24 Monotone convergence theorem for nets 106 Multiplicity free operators 231 Multiplicity theory 231—234 n-particle subspace 208 n-point function 66 Nelson’s analytic vector theorem 202 Nelson’s commutator theorem 193 nonrelativistic quantum mechanics 15 Norm resolvent sense, convergence in 284—291 Normal bundle 120 Normal operator 246 Normalized tangent functional 240 Norms consistent 35 Norms consistent, interpolating 37 Nuclear theorem 141 144 Number operator 142 204 208 220 Nussbaum’s lemma 201 of an unbounded operator 249 One-parameter unitary group 265 Open mapping theorem 82 132 Operator positively preserving 186 Operator positively preserving, relatively bounded 162 Operator positively preserving, self-adjoint 187 255 Operator positively preserving, symmetric 255 192 Oscillatory integral 100 Paley — Wiener theorems 16 17 18 23 109 Parallelogram law 38 63 Parseval’s relation 45 46 Partial isometry 197 PCT theorem 69 Phase function 99 Phase space 313 Plancherel theorem 10 Poincare group 63 Poincare Invariance 65 Poisson bracket 314 Polarization identity 63 Positive distribution 162 Positive linear functional 106 Positive operator 195 Positive quadratic form 276 Positive type distribution 14 Positive type distribution, function 12 Positive type distribution, weak 14 Positivity preserving operator 186 Principle of uniform boundedness 81 132 Product formula 295—297 245 Product of distributions 90 Product topology 94 Projection 187 Projection theorem 42 Projection valued measure 234—235 262—263 Projection, orthogonal 187 Propagator 60 282 Pseudo-differential operator 119 q-space 228 Quadratic form 276 Quantum field 64 (see also “Free field and Canonical free field”) Quantum field theory 62 quantum mechanics 302—305 Quasi-analytic vector 327 Radon — Nikodym theorem 25 Reconstruction theorem 114 Regular directed point 92 Regular point 88 Regularity of the field 64 Regularity, Schroedinger's equation 54 Regularity, tempered distributions 139 144 Regularity, theorem (Weyl’s lemma) 53 Regularly imbedded submanifold of codimension k 78 Relatively bounded form 168 Relatively bounded operator 162 Relatively compact 340 Relativistic invariance 62 Resolvent 188 253 Resolvent set 188 253 Restricted Lorentz group 63 Restricted Poincare group 63 Riemann — Lebesgue lemma 10 Riesz lemma 43 41—44 Riesz — Fischer theorem 18 24 68 Riesz — Thorin theorem 27 Rigged Hilbert space 44 Rollnik potential 170 Scalar quantum field theory 62 212 Scale of spaces 278 44 Schrodinger equation 303 Schrodinger representation 274 Schwartz space 133 Schwarz inequality 38 Schwinger functions 114 Second quantization 302 308 208 Segal field operator 209 Segal quantization 209 Self-adjoint operator bounded 187
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