Verfügbarkeit: Quantum physics | Technische Universität München

Quantum physics: a functional integral point of view

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Bibliographische Detailangaben
Beteiligte Personen:	Glimm, James 1934- (VerfasserIn), Jaffe, Arthur 1937- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York ; Berlin ; Heidelberg Springer-Verlag [1987]
Ausgabe:	Second edition
Schlagwörter:	Champs, Théorie quantique des Kwantummechanica Kwantumveldentheorie Physique statistique Quanta, Théorie des Statistische mechanica Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik Funktionalintegration Quantenfeldtheorie Quantenphysik Statistische Physik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001504608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Umfang:	XXII, 535 Seiten Diagramme
ISBN:	0387964762 3540964762 0387964770 3540964770 9780387964775

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Datensatz im Suchindex

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adam_text	James Glimm Arthur Jaffe Quantum Physics A Functional Integral Point of View Second Edition With 51 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Contents Preface v Introduction - xiii Conventions and Formulas xvii List of Symbols xix PART I An Introduction to Modern Physics 1 Quantum Theory 3 1 1 Overview - 3 1 2 Classical Mechanics 3 1 3 Quantum Mechanics 7 1 4 Interpretation 11 1 5 The Simple Harmonic Oscillator 12 1 6 Coulomb Potentials 20 J 7 The Hydrogen Atom •, 24 i 8 The Need for Quantum Fields 26 2 Classical Statistical Mechanics t 28 2 1 Introduction 28 2 2 The Classical Ensembles 30 2 3 The Ising Model and Lattice Fields 36 2 4 Series Expansion Methods 37 vii viii Contents 3 The Feynman-Kac Formula 43 3 1 Wiener Measure 43 3 2 The Feynman-Kac Formula 47 3 3 Uniqueness of the Ground State 51 3 4 The Renormalized Feynman-Kac Formula 52 Correlation Inequalities and the Lee-Yang Theorem 56 4 1 Griffiths Inequalities 57 4 2 The Infinite Volume Limit 59 43C Inequalities 60 4 4 The FKG Inequality 64 4 5 The Lee-Yang Theorem 66 4 6 Analyticity of the Free Energy 69 4 7 Two Component Spins 71 Phase Transitions and Critical Points 73 5 1 Pure and Mixed Phases 73 5 2 The Mean Field Picture 75 5 3 Symmetry Breaking 78 5 4 The Droplet Model and Peierls Argument 81 5 5 Some Examples 86 Field Theory 90 6 1 Axioms 90 (i) Euclidean Axioms 90 (ii) Minkowski Space Axioms 97 6 2 The Fr,ee Field 100 6 3 Fock Space and Wick Ordering 106 6 4 Canonical Quantization 111 6 5 Fefmions 115 6 6 Interacting Fields 118 Appendix to Part I Hilbert Space Operators and Functional Integrals _ 122 A 1 Bounded and Unbounded Operators on Hilbert Space 122 A 2 Positive Operators arid Bilinear Forms 129 A 3 Trace Class Operators and Nuclear Spaces 132 A 4 Gaussian Measures 136 A 5 The Lie Product Theorem 144 A 6 The Bochner-Minlos Theorem 148 A 7 Stochastic Integrals 150 A 8 Stochastic Differential Equations 153 Contents ix PART II Function S,pace Integrals 7 Covariance Operator = Green s Function = Resolvent Kernel = Euclidean Propagator = Fundamental Solution 159 7 1 Introduction 159 7 2 The Free Covariance 161 7 3 Periodic Boundary Conditions 163 7 4 Neumann Boundary Conditions 164 7 5 Dirichlet Boundary Conditions 165 7 6 Change of Boundary Conditions 166 7 7 Covariance Operator Inequalities 166 7 8 More General Dirichlet Data 168 7 9 Regularity of CB 173 7 10 Reflection Positivity 177 8 Quantization = Integration over Function Space 180 8 1 Introduction 180 8 2 Feynman Graphs 181 8 3 Wick Products 183 8 4 Formal Perturbation Theory 186 8 5 Estimates on Gaussian Integrals 188 8 6 Non-Gaussian Integrals, d=2 193 8 7 Finite Dimensional Approximations 199 9 Calculus and Renormalization on Function Space 202 91A Compilation of Useful Formulas 202 (i) Wick Product Identities 202 (ii) Gaussian Integrals 205 (iii) Integration by Parts 207 (iv) Limits of Measures 208 9 2 Infinitesimal Change of Covariance 210 9 3 Quadratic Perturbations 211 9 4 Perturbative Renormalization 215 9 5 Lattice Laplace and Covariance Operators 219 9 6 Lattice Approximation of P{4 )2 Measures 225 Estimates Independent of Dimension 229 10 1 Introduction , 229 10 2 Correlation Inequalities for P( / )2 Fields 229 10 3 Dirichlet or Neumann Monotonicity and Decoupling 231 10 4 Reflection Positivity 234 10 5 Multiple Reflections 236 10 6 Nonsymmetric Reflections 242 x Contents 11 Fields Without Cutoffs 249 11 1 Introduction 249 11 2 Monotone Convergence 249 11 3 Upper Bounds 251 12 Regularity and Axioms 255 12 1 Introduction 255 12 2 Integration by Parts 256 12 3 Nonlocal f J Bounds 259 12 4 Uniformity in the Volume 261 12 5 Regularity of the P(4 )2 Field 265 PART III The Physics of Quantum Fields 13 Scattering Theory: Time-Dependent Methods 273 13 1 Introduction 273 13 2 Multiparticle Potential Scattering 276 13 3 The Wave Operator for Quantum Fields 280 13 4 Wave Packets for Free Particles 283 13 5 The Haag-Ruelle Theory 285 14 Scattering Theory: Time-Independent Methods 292 14 1 Time-Ordered Correlation Functions 292 14 2 The S Matrix 295 14 3 Renormalization 296 14 4 The Bethe-Salpeter Kernel 300 15 The Magnetic Moment of the Electron 306 15 1 Classical Magnetic Moments 306 15 2 The Fine Structure of the Hydrogen Atom and the Dirac Equation 308 15 3 The Dirac Theory 310 15 4 The Anomalous Moment 312 15 5 The Hyperfine Structure and the Lamb Shift of the Hydrogen Atom • 315 16 Phase Transitions 316 16 1 Introduction 316 16 2 The Two Phase Region 320 Contents xi 16 3 Symmetry JLJnbroken, d=2 330 16 4 Symmetry Broken, 3 d 333 17 The 4 * Critical Point 339 17 1 Elementary Considerations 339 17 2 The Absence of Even Bound States 340 17 3 A Bound on the Coupling Constant Aphys 342 17 4 Existence of Particles and a Bound on dm2 /do 344 17 5 Existence of the f * Critical Point 345 17 6 Continuity of dfi at the Critical Point 348 17 7 Critical Exponents 349 17 8 t 1 351 17 9 The Scaling Limit 353 17 10 The Conjecture P6 0 354 18 The Cluster Expansion 356 18 1 Introduction 356 18 2 The Cluster Expansion 359 18 3 Clustering and Analyticity 365 18 4 Convergence: The Main Ideas 367 18 5 An Equation of Kirkwood-Salsburg Type 370 18 6 Covariance Operators 371 18 7 Convergence: The ProofrCompleted 376 19 From Path Integrals to Quantum Mechanics 379 19 1 Reconstruction of Quantum Fields 379 19 2 The Feynman-Kac Formula 382 19 3 Self-Adjoint Fields 384 19 4 Commutators 385 19 5 Lorentz Covariance 389 19 6 Locality 392 19 7 Uniqueness of the Vacuum 393 !0 The Polymer Expansion 398 20 1 Introduction 398 20 2 Activity Expansions and Connected Polymers 399 20 3 Convergence of the Polymer Expansion 405 20 4 The Tree Graph Decay of Correlations and the Existence of the Free Energy 410 20 5 Polymer Expansion Examples t 411 (i) The High Temperature Ising Model 412 (ii) The Weak Coupling of Euclidean Quantum Fields 413 (iii) Mayer Expansion of the Grand Canonical Partition Function 416 (iv) Low Temperature Ising Model 416 xii Contents 21 Random Path Representations 419 21 1 Random Walks and the Laplacian 420 21 2 Local Stopping Times 421 21 3 Gaussian Integration by Parts 423 21 4 Non-Gaussian Integration by Parts 424 21 5 41* Correlation Inequalities 427 21 6 The j * Noninteraction Theorem 433 22 Constructive Gauge Theory and Phase Cell Localization 437 22 1 Introduction 437 22 2 Regularization and Lattice Approximations 442 22 3 Reflection Positivity of the Lattice Approximation 446 22 4 Phase Cell Localization and Exact Renormalization Transformations 447 22 5 Infra-Red Behavior 451 22 6 Lattice Maxwell Theory—An Example of Renormalization 454 22 7 Nonabelian Gauge Models 457 23 Further Directions 460 23 1 The $ Model 460 23 2 Borel Summability 461 23/3 Euclidean Fermi Fields 462 23 4 Yukawa Interactions 463 23 5 Low Temperature Expansions and Phase Transitions 464 23 6 Debye Screening and the Sine-Gordon Transformation 465 23 7 Dipoles Don t Screen 468 23 8 Solitons 470 Bibliography 472 Index 529
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publishDateSort	1987
publisher	Springer-Verlag
record_format	marc
spellingShingle	Glimm, James 1934- Jaffe, Arthur 1937- Quantum physics a functional integral point of view Champs, Théorie quantique des Champs, Théorie quantique des ram Kwantummechanica gtt Kwantumveldentheorie gtt Physique statistique Physique statistique ram Quanta, Théorie des ram Statistische mechanica gtt Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik (DE-588)4047989-4 gnd Funktionalintegration (DE-588)4155674-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantentheorie (DE-588)4047992-4 gnd Statistische Physik (DE-588)4057000-9 gnd
subject_GND	(DE-588)4047989-4 (DE-588)4155674-4 (DE-588)4047984-5 (DE-588)4266670-3 (DE-588)4047992-4 (DE-588)4057000-9
title	Quantum physics a functional integral point of view
title_auth	Quantum physics a functional integral point of view
title_exact_search	Quantum physics a functional integral point of view
title_full	Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe
title_fullStr	Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe
title_full_unstemmed	Quantum physics a functional integral point of view James Glimm ; Arthur Jaffe
title_short	Quantum physics
title_sort	quantum physics a functional integral point of view
title_sub	a functional integral point of view
topic	Champs, Théorie quantique des Champs, Théorie quantique des ram Kwantummechanica gtt Kwantumveldentheorie gtt Physique statistique Physique statistique ram Quanta, Théorie des ram Statistische mechanica gtt Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik (DE-588)4047989-4 gnd Funktionalintegration (DE-588)4155674-4 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Quantenphysik (DE-588)4266670-3 gnd Quantentheorie (DE-588)4047992-4 gnd Statistische Physik (DE-588)4057000-9 gnd
topic_facet	Champs, Théorie quantique des Kwantummechanica Kwantumveldentheorie Physique statistique Quanta, Théorie des Statistische mechanica Théorie quantique Quantentheorie Quantum field theory Quantum theory Statistical physics Quantenmechanik Funktionalintegration Quantenfeldtheorie Quantenphysik Statistische Physik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001504608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT glimmjames quantumphysicsafunctionalintegralpointofview AT jaffearthur quantumphysicsafunctionalintegralpointofview

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