Applied mathematical methods in theoretical physics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH-Verl.
2009
|
| Edition: | 2., enl. and improved ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XX, 578 S. graph. Darst. |
| ISBN: | 9783527409365 |
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Record in the Search Index
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| adam_text |
IMAGE 1
VII
CONTENTS
PREFACE XI
INTRODUCTION XV
1 FUNCTION SPACES, LINEAR OPERATORS, AND GREEN'S FUNCTIONS 1 1.1
FUNCTION SPACES 1 1.2 ORTHONORMAL SYSTEM OF FUNCTIONS 3 1.3 LINEAR
OPERATORS 5
1.4 EIGENVALUES AND EIGENFUNCTIONS 7 1.5 THE FREDHOLM ALTERNATIVE 9 1.6
SELF-ADJOINT OPERATORS 12 1.7 GREEN'S FUNCTIONS FOR DIFFERENTIAL
EQUATIONS 14 1.8 REVIEW OF COMPLEX ANALYSIS 18 1.9 REVIEW OF FOURIER
TRANSFORM 25
2 INTEGRAL EQUATIONS AND GREEN'S FUNCTIONS 31 2.1 INTRODUCTION TO
INTEGRAL EQUATIONS 31 2.2 RELATIONSHIP OF INTEGRAL EQUATIONS WITH
DIFFERENTIAL EQUATIONS AND GREEN'S FUNCTIONS 37 2.3 STURM-IIOUVILLE
SYSTEM 43 2.4 GREEN'S FUNCTION FOR TIME-DEPENDENT SCATTERING PROBLEM 47
2.5 LIPPMANN-SCHWINGER EQUATION 51 2.6 SCALAR FIELD INTERACTING WITH
STATIC SOURCE 62 2.7 PROBLEMS FOR CHAPTER 2 67
3 INTEGRAL EQUATIONS OF THE VOLTERRA TYPE 205 3.1 ITERATIVE SOLUTION TO
VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND 105
3.2 SOLVABLE CASES OF THE VOLTERRA INTEGRAL EQUATION 108 3.3 PROBLEMS
FOR CHAPTER 3 112
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/993261353
DIGITALISIERT DURCH
IMAGE 2
VLLLL CONTENTS
4 INTEGRAL EQUATIONS OF THE FREDHOLM TYPE 117
4.1 ITERATIVE SOLUTION TO THE FREDHOLM INTEGRAL EQUATION OF THE SECOND
KIND 117 4.2 RESOLVENT KERNEL 120 4.3 PINCHERLE-GOURSAT KERNEL 123 4.4
FREDHOLM THEORY FOR A BOUNDED KERNEL 127 4.5 SOLVABLE EXAMPLE 134 4.6
FREDHOLM INTEGRAL EQUATION WITH A TRANSLATION KERNEL 136 4.7 SYSTEM OF
FREDHOHN INTEGRAL EQUATIONS OF THE SECOND KIND 143
4.8 PROBLEMS FOR CHAPTER 4 143
5 HILBERT-SCHMIDT THEORY OF SYMMETRIC KERNEL 153 5.1 REAL AND SYMMETRIC
MATRIX 153 5.2 REAL AND SYMMETRIC KERNEL 155 5.3 BOUNDS ON THE
EIGENVALUES 166 5.4 RAYLEIGH QUOTIENT 169 5.5 COMPLETENESS OF STURM-
IIOUVILLE EIGENFUNCTIONS 172 5.6 GENERALIZATION OF HILBERT-SCHMIDT
THEORY 174 5.7 GENERALIZATION OF THE STURM-IIOUVILLE SYSTEM 181 5.8
PROBLEMS FOR CHAPTER 5 187
6 SINGULAR INTEGRAL EQUATIONS OF THE CAUCHY TYPE 193 6.1 HUBERT PROBLEM
193 6.2 CAUCHY INTEGRAL EQUATION OF THE FIRST KIND 197 6.3 CAUCHY
INTEGRAL EQUATION OF THE SECOND KIND 201
6.4 CARLEMAN INTEGRAL EQUATION 205 6.5 DISPERSION RELATIONS 212 6.6
PROBLEMS FOR CHAPTER 6 218
7 WIENER-HOPF METHOD AND WIENER-HOPF INTEGRAL EQUATION 223 7.1 THE
WIENER-HOPF METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS 223 7.2
HOMOGENEOUS WIENER-HOPF INTEGRAL EQUATION OF THE SECOND KIND 237
7.3 GENERAL DECOMPOSITION PROBLEM 252 7.4 INHOMOGENEOUS WIENER-HOPF
INTEGRAL EQUATION OF THE SECOND KIND 262 7.5 TOEPLITZ MATRIX AND
WIENER-HOPF SUM EQUATION 272 7.6 WIENER-HOPF INTEGRAL EQUATION OF THE
FIRST KIND AND DUAL INTEGRAL
EQUATIONS 281
7.7 PROBLEMS FOR CHAPTER 7 285
8 NONLINEAR INTEGRAL EQUATIONS 295 8.1 NONLINEAR INTEGRAL EQUATION OF
THE VOLTERRA TYPE 295 8.2 NONLINEAR INTEGRAL EQUATION OF THE FREDHOLM
TYPE 299 8.3 NONLINEAR INTEGRAL EQUATION OF THE HAMMERSTEIN TYPE 303 8.4
PROBLEMS FOR CHAPTER 8 305
IMAGE 3
CONTENTS IX
9 CALCULUS OF VARIATIONS: FUNDAMENTALS 309
9.1 HISTORICAL BACKGROUND 309 9.2 EXAMPLES 313
9.3 EULER EQUATION 324 9.4 GENERALIZATION OF THE BASIC PROBLEMS 319 9.5
MORE EXAMPLES 323 9.6 DIFFERENTIAL EQUATIONS, INTEGRAL EQUATIONS, AND
EXTREMIZATION OF
INTEGRALS 326
9.7 THE SECOND VARIATION 330 9.8 WEIERSTRASS-ERDMANN CORNER RELATION 345
9.9 PROBLEMS FOR CHAPTER 9 349
10 CALCULUS OF VARIATIONS: APPLICATIONS 353 10.1 HAMILTON-JACOBI
EQUATION AND QUANTUM MECHANICS 353 10.2 FEYNMAN'S ACTION PRINCIPLE IN
QUANTUM THEORY 361 10.3 SCHWINGER'S ACTION PRINCIPLE IN QUANTUM THEORY
368 10.4 SCHWINGER-DYSON EQUATION IN QUANTUM FIELD THEORY 371 10.5
SCHWINGER-DYSON EQUATION IN QUANTUM STATISTICAL MECHANICS 385 10.6
FEYNMAN'S VARIATIONAL PRINCIPLE 395 10.7 POINCARE TRANSFORMATION AND
SPIN 407 10.8 CONSERVATION LAWS AND NOETHER'S THEOREM 411 10.9 WEYL'S
GAUGE PRINCIPLE 418 10.10 PATH INTEGRAL QUANTIZATION OF GAUGE FIELD I
437
10.11 PATH INTEGRAL QUANTIZATION OF GAUGE FIELD II 454 10.12 BRST
INVARIANCE AND RENORMALIZATION 468 10.13 ASYMPTOTIC DISASTER IN QED 475
10.14 ASYMPTOTIC FREEDOM IN QCD 479 10.15 RENORMALIZATION GROUP
EQUATIONS 487 10.16 STANDARD MODEL 499 10.17 LATTICE GAUGE FIELD THEORY
AND QUARK CONFINEMENT 518 10.18 WKB APPROXIMATION IN PATH INTEGRAL
FORMALISM 523 10.19 HARTREE-FOCK EQUATION 526 10.20 PROBLEMS FOR CHAPTER
10 529
REFERENCES 567
INDEX 573 |
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| discipline | Chemie / Pharmazie Physik Mathematik |
| edition | 2., enl. and improved ed. |
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| isbn | 9783527409365 |
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| spelling | Masujima, Michio 1949- Verfasser (DE-588)121811212 aut Applied mathematical methods in theoretical physics Michio Masujima 2., enl. and improved ed. Weinheim Wiley-VCH-Verl. 2009 XX, 578 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3261161&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018663371&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Applied mathematical methods in theoretical physics |
| title_auth | Applied mathematical methods in theoretical physics |
| title_exact_search | Applied mathematical methods in theoretical physics |
| title_full | Applied mathematical methods in theoretical physics Michio Masujima |
| title_fullStr | Applied mathematical methods in theoretical physics Michio Masujima |
| title_full_unstemmed | Applied mathematical methods in theoretical physics Michio Masujima |
| title_short | Applied mathematical methods in theoretical physics |
| title_sort | applied mathematical methods in theoretical physics |
| topic | Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik - Lehrbuch Mathematische Physik Mathematical physics Lehrbuch |
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