Field theory: a path integral approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore u.a.
World Scientific
2006
|
| Edition: | 2. ed. |
| Series: | World Scientific lecture notes in physics
75 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 361 S. graph. Darst. |
| ISBN: | 9812568484 9789812568489 9812568476 |
Staff View
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Record in the Search Index
| _version_ | 1804135597654147072 |
|---|---|
| adam_text | STEVEN ROMAN FIELD THEORY SECOND EDITION WITH 18 ILLUSTRATIONS ^J
SPRINGER CONTENTS PREFACE VII CONTENTS IX 0 PRELIMINARIES 1 0.1 LATTICES
1 0.2 GROUPS 2 0.3 THE SYMMETRIC GROUP Y 10 0.4 RINGS... 10 0.5 INTEGRAL
DOMAINS 14 0.6 UNIQUE FACTORIZATION DOMAINS 16 0.7 PRINCIPAL IDEAL
DOMAINS 16 0.8 EUCLIDEAN DOMAINS 17 0.9 TENSOR PRODUCTS 17 EXERCISES 19
PART I*FIELD EXTENSIONS 1 POLYNOMIALS 23 1.1 POLYNOMIALS OVER A RING 23
1.2 PRIMITIVE POLYNOMIALS AND IRREDUCIBILITY 24 1.3 THE DIVISION
ALGORITHM AND ITS CONSEQUENCES 27 1.4 SPLITTING FIELDS . 32 1.5 THE
MINIMAL POLYNOMIAL 32 1.6 MULTIPLE ROOTS 33 1.7 TESTING FOR
IRREDUCIBILITY 35 EXERCISES 38 2 FIELD EXTENSIONS 41 2.1 THE LATTICE OF
SUBFIELDS OF A FIELD 41 2.2 TYPES OF FIELD EXTENSIONS 42 2.3 FINITELY
GENERATED EXTENSIONS 46 2.4 SIMPLE EXTENSIONS 47 2.5 FINITE EXTENSIONS
53 2.6 ALGEBRAIC EXTENSIONS 54 CONTENTS 2.7 ALGEBRAIC CLOSURES 56 2.8
EMBEDDINGS AND THEIR EXTENSIONS 58 2.9 SPLITTING FIELDS AND NORMAL
EXTENSIONS 63 EXERCISES 66 3 EMBEDDINGS AND SEPARABILITY 73 3.1 RECAP
AND A USEFUL LEMMA 73 3.2 THE NUMBER OF EXTENSIONS: SEPARABLE DEGREE 75
3.3 SEPARABLE EXTENSIONS 77 3.4 PERFECT FIELDS 84 3.5 PURE
INSEPARABILITY 85 *3.6 SEPARABLE AND PURELY INSEPARABLE CLOSURES 88
EXERCISES 91 4 ALGEBRAIC INDEPENDENCE 93 4.1 DEPENDENCE RELATIONS 93 4.2
ALGEBRAIC DEPENDENCE 96 4.3 TRANSCENDENCE BASES 100 *4.4 SIMPLE
TRANSCENDENTAL EXTENSIONS 105 EXERCISES 108 PART II*GALOIS THEORY 5
GALOIS THEORY I: AN HISTORICAL PERSPECTIVE 113, 5.1 THE QUADRATIC
EQUATION 113 5.2 THE CUBIC AND QUARTIC EQUATIONS 114 5.3 HIGHER-DEGREE
EQUATIONS. 116 5.4 NEWTON S CONTRIBUTION: SYMMETRIC POLYNOMIALS 117 5.5
VANDERMONDE 119 5.6 LAGRANGE 121 5.7 GAUSS 124 5.8 BACK TO LAGRANGE 128
5.9 GALOIS 130 5.10 A VERY BRIEF LOOK AT THE LIFE OF GALOIS 135 6 GALOIS
THEORY II: THE THEORY 137 6.1 GALOIS CONNECTIONS 137 6.2 THE GALOIS
CORRESPONDENCE 143 6.3 WHO S CLOSED? * 148 6.4 NORMAL SUBGROUPS AND
NORMAL EXTENSIONS 154 6.5 MORE ON GALOIS GROUPS 159 6.6 ABELIAN AND
CYCLIC EXTENSIONS 164 *6.7 LINEAR DISJOINTNESS 165 EXERCISES 168 7
GALOIS THEORY III: THE GALOIS GROUP OF A POLYNOMIAL 173 7.1 THE GALOIS
GROUP OF A POLYNOMIAL 173 7.2 SYMMETRIC POLYNOMIALS 174 7.3 THE
FUNDAMENTAL THEOREM OF ALGEBRA 179 CONTENTS XI 7.4 THE DISCRIMINANT OF A
POLYNOMIAL 180 7.5 THE GALOIS GROUPS OF SOME SMALL-DEGREE POLYNOMIALS
182 EXERCISES...; 193 8 A FIELD EXTENSION AS A VECTOR SPACE 197 8.1 THE
NORM AND THE TRACE 197 . *8.2 CHARACTERIZING BASES 202 *8.3 THE NORMAL
BASIS THEOREM 206 EXERCISES 208 9 FINITE FIELDS I: BASIC PROPERTIES 211
9.1 FINITE FIELDS REDUX 211 9.2 FINITE FIELDS AS SPLITTING FIELDS 212
9.3 THE SUBFIELDS OF A FINITE FIELD 213 9.4 THE MULTIPLICATIVE STRUCTURE
OF A FINITE FIELD 214 9.5 THE GALOIS GROUP OF A FINITE FIELD 215 9.6
IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS 215 *9.7 NORMAL BASES 218
*9.8 THE ALGEBRAIC CLOSURE OF A FINITE FIELD 219 EXERCISES 223 10 FINITE
FIELDS II: ADDITIONAL PROPERTIES 225 10.1 FINITE FIELD ARITHMETIC 225
*10.2 THE NUMBER OF IRREDUCIBLE POLYNOMIALS 232 *10.3 POLYNOMIAL
FUNCTIONS 234 . *10.4 LINEARIZED POLYNOMIALS 236 EXERCISES 238 11 THE
ROOTS OF UNITY 239 11.1 ROOTS OF UNITY 239 11.2 CYCLOTOMIC EXTENSIONS
241 *11.3 NORMAL BASES AND ROOTS OF UNITY 250 *11.4 WEDDERBURN S THEOREM
251 *11.5 REALIZING GROUPS AS GALOIS GROUPS 253 EXERCISES . 257 12
CYCLIC EXTENSIONS 261 12.1 CYCLIC EXTENSIONS 261 12.2 EXTENSIONS OF
DEGREE CHAR(I^) 265 EXERCISES 266 13 SOLVABLE EXTENSIONS 269 13.1
SOLVABLE GROUPS 269 13.2 SOLVABLE EXTENSIONS 270 13.3 RADICAL EXTENSIONS
273 13.4 SOLVABILITY BY RADICALS 274 13.5 SOLVABLE EQUIVALENT TO
SOLVABLE BY RADICALS 276 13.6 NATURAL AND ACCESSORY IRRATIONALITIES 278
13.7 POLYNOMIAL EQUATIONS 280 XII CONTENTS EXERCISES 282 PART III*THE
THEORY OF BINOMIALS 14 BINOMIALS 289 14.1 IRREDUCIBILITY 289 14.2 THE
GALOIS GROUP OF A BINOMIAL 296 *14.3 THE INDEPENDENCE OF IRRATIONAL
NUMBERS 304 EXERCISES 307 15 FAMILIES OF BINOMIALS 309 15.1 THE
SPLITTING FIELD 309 15.2 DUAL GROUPS AND PAIRINGS 310 15.3 KUMMER THEORY
312 EXERCISES 316 APPENDIX: MOBIUS INVERSION 319 PARTIALLY ORDERED SETS
319 THE INCIDENCE ALGEBRA OF A PARTIALLY ORDERED SET 320 CLASSICAL
MOBIUS INVERSION 324 MULTIPLICATIVE VERSION OF MOBIUS INVERSION 325
REFERENCES T 327 INDEX 329
|
| adam_txt |
STEVEN ROMAN FIELD THEORY SECOND EDITION WITH 18 ILLUSTRATIONS ^J
SPRINGER CONTENTS PREFACE VII CONTENTS IX 0 PRELIMINARIES 1 0.1 LATTICES
1 0.2 GROUPS 2 0.3 THE SYMMETRIC GROUP Y 10 0.4 RINGS. 10 0.5 INTEGRAL
DOMAINS 14 0.6 UNIQUE FACTORIZATION DOMAINS 16 0.7 PRINCIPAL IDEAL
DOMAINS 16 0.8 EUCLIDEAN DOMAINS 17 0.9 TENSOR PRODUCTS 17 EXERCISES 19
PART I*FIELD EXTENSIONS 1 POLYNOMIALS 23 1.1 POLYNOMIALS OVER A RING 23
1.2 PRIMITIVE POLYNOMIALS AND IRREDUCIBILITY 24 1.3 THE DIVISION
ALGORITHM AND ITS CONSEQUENCES 27 1.4 SPLITTING FIELDS '. 32 1.5 THE
MINIMAL POLYNOMIAL 32 1.6 MULTIPLE ROOTS 33 1.7 TESTING FOR
IRREDUCIBILITY 35 EXERCISES 38 2 FIELD EXTENSIONS 41 2.1 THE LATTICE OF
SUBFIELDS OF A FIELD 41 2.2 TYPES OF FIELD EXTENSIONS 42 2.3 FINITELY
GENERATED EXTENSIONS 46 2.4 SIMPLE EXTENSIONS 47 2.5 FINITE EXTENSIONS
53 2.6 ALGEBRAIC EXTENSIONS 54 CONTENTS 2.7 ALGEBRAIC CLOSURES 56 2.8
EMBEDDINGS AND THEIR EXTENSIONS 58 2.9 SPLITTING FIELDS AND NORMAL
EXTENSIONS 63 EXERCISES 66 3 EMBEDDINGS AND SEPARABILITY 73 3.1 RECAP
AND A USEFUL LEMMA 73 3.2 THE NUMBER OF EXTENSIONS: SEPARABLE DEGREE 75
3.3 SEPARABLE EXTENSIONS 77 3.4 PERFECT FIELDS 84 3.5 PURE
INSEPARABILITY 85 *3.6 SEPARABLE AND PURELY INSEPARABLE CLOSURES 88
EXERCISES 91 4 ALGEBRAIC INDEPENDENCE 93 4.1 DEPENDENCE RELATIONS 93 4.2
ALGEBRAIC DEPENDENCE 96 4.3 TRANSCENDENCE BASES 100 *4.4 SIMPLE
TRANSCENDENTAL EXTENSIONS 105 EXERCISES 108 PART II*GALOIS THEORY 5
GALOIS THEORY I: AN HISTORICAL PERSPECTIVE 113, 5.1 THE QUADRATIC
EQUATION 113 5.2 THE CUBIC AND QUARTIC EQUATIONS 114 5.3 HIGHER-DEGREE
EQUATIONS. 116 5.4 NEWTON'S CONTRIBUTION: SYMMETRIC POLYNOMIALS 117 5.5
VANDERMONDE 119 5.6 LAGRANGE 121 5.7 GAUSS 124 5.8 BACK TO LAGRANGE 128
5.9 GALOIS 130 5.10 A VERY BRIEF LOOK AT THE LIFE OF GALOIS 135 6 GALOIS
THEORY II: THE THEORY 137 6.1 GALOIS CONNECTIONS 137 6.2 THE GALOIS
CORRESPONDENCE 143 6.3 WHO'S CLOSED? * 148 6.4 NORMAL SUBGROUPS AND
NORMAL EXTENSIONS 154 6.5 MORE ON GALOIS GROUPS 159 6.6 ABELIAN AND
CYCLIC EXTENSIONS 164 *6.7 LINEAR DISJOINTNESS 165 EXERCISES 168 7
GALOIS THEORY III: THE GALOIS GROUP OF A POLYNOMIAL 173 7.1 THE GALOIS
GROUP' OF A POLYNOMIAL 173 7.2 SYMMETRIC POLYNOMIALS 174 7.3 THE
FUNDAMENTAL THEOREM OF ALGEBRA 179 CONTENTS XI 7.4 THE DISCRIMINANT OF A
POLYNOMIAL 180 7.5 THE GALOIS GROUPS OF SOME SMALL-DEGREE POLYNOMIALS
182 EXERCISES.; 193 8 A FIELD EXTENSION AS A VECTOR SPACE 197 8.1 THE
NORM AND THE TRACE 197 . *8.2 CHARACTERIZING BASES 202 *8.3 THE NORMAL
BASIS THEOREM 206 EXERCISES 208 9 FINITE FIELDS I: BASIC PROPERTIES 211
9.1 FINITE FIELDS REDUX 211 9.2 FINITE FIELDS AS SPLITTING FIELDS 212
9.3 THE SUBFIELDS OF A FINITE FIELD 213 9.4 THE MULTIPLICATIVE STRUCTURE
OF A FINITE FIELD 214 9.5 THE GALOIS GROUP OF A FINITE FIELD 215 9.6
IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS 215 *9.7 NORMAL BASES 218
*9.8 THE ALGEBRAIC CLOSURE OF A FINITE FIELD 219 EXERCISES 223 10 FINITE
FIELDS II: ADDITIONAL PROPERTIES 225 10.1 FINITE FIELD ARITHMETIC 225
*10.2 THE NUMBER OF IRREDUCIBLE POLYNOMIALS 232 *10.3 POLYNOMIAL
FUNCTIONS 234 . *10.4 LINEARIZED POLYNOMIALS 236 EXERCISES 238 11 THE
ROOTS OF UNITY 239 11.1 ROOTS OF UNITY 239 11.2 CYCLOTOMIC EXTENSIONS
241 *11.3 NORMAL BASES AND ROOTS OF UNITY 250 *11.4 WEDDERBURN'S THEOREM
251 *11.5 REALIZING GROUPS AS GALOIS GROUPS 253 EXERCISES '. 257 12
CYCLIC EXTENSIONS 261 12.1 CYCLIC EXTENSIONS 261 12.2 EXTENSIONS OF
DEGREE CHAR(I^) 265 EXERCISES 266 13 SOLVABLE EXTENSIONS 269 13.1
SOLVABLE GROUPS 269 13.2 SOLVABLE EXTENSIONS 270 13.3 RADICAL EXTENSIONS
273 13.4 SOLVABILITY BY RADICALS 274 13.5 SOLVABLE EQUIVALENT TO
SOLVABLE BY RADICALS 276 13.6 NATURAL AND ACCESSORY IRRATIONALITIES 278
13.7 POLYNOMIAL EQUATIONS 280 XII CONTENTS EXERCISES 282 PART III*THE
THEORY OF BINOMIALS 14 BINOMIALS 289 14.1 IRREDUCIBILITY 289 14.2 THE
GALOIS GROUP OF A BINOMIAL 296 *14.3 THE INDEPENDENCE OF IRRATIONAL
NUMBERS 304 EXERCISES 307 15 FAMILIES OF BINOMIALS 309 15.1 THE
SPLITTING FIELD 309 15.2 DUAL GROUPS AND PAIRINGS 310 15.3 KUMMER THEORY
312 EXERCISES 316 APPENDIX: MOBIUS INVERSION 319 PARTIALLY ORDERED SETS
319 THE INCIDENCE ALGEBRA OF A PARTIALLY ORDERED SET 320 CLASSICAL
MOBIUS INVERSION 324 MULTIPLICATIVE VERSION OF MOBIUS INVERSION 325
REFERENCES T 327 INDEX 329 |
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| dewey-search | 530.14/3 |
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| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T15:30:16Z |
| indexdate | 2024-07-09T20:43:02Z |
| institution | BVB |
| isbn | 9812568484 9789812568489 9812568476 |
| language | English |
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| publishDate | 2006 |
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| publisher | World Scientific |
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| series | World Scientific lecture notes in physics |
| series2 | World Scientific lecture notes in physics |
| spelling | Das, Ashok 1953- Verfasser (DE-588)13395157X aut Field theory a path integral approach Ashok Das 2. ed. Singapore u.a. World Scientific 2006 XIV, 361 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific lecture notes in physics 75 Champs, Théorie quantique des Intégrales de chemin Path integrals Quantum field theory Feldtheorie (DE-588)4016698-3 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 s Pfadintegral (DE-588)4173973-5 s 1\p DE-604 Feldtheorie (DE-588)4016698-3 s 2\p DE-604 World Scientific lecture notes in physics 75 (DE-604)BV000819327 75 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014957484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Das, Ashok 1953- Field theory a path integral approach World Scientific lecture notes in physics Champs, Théorie quantique des Intégrales de chemin Path integrals Quantum field theory Feldtheorie (DE-588)4016698-3 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4016698-3 (DE-588)4047984-5 (DE-588)4173973-5 |
| title | Field theory a path integral approach |
| title_auth | Field theory a path integral approach |
| title_exact_search | Field theory a path integral approach |
| title_exact_search_txtP | Field theory a path integral approach |
| title_full | Field theory a path integral approach Ashok Das |
| title_fullStr | Field theory a path integral approach Ashok Das |
| title_full_unstemmed | Field theory a path integral approach Ashok Das |
| title_short | Field theory |
| title_sort | field theory a path integral approach |
| title_sub | a path integral approach |
| topic | Champs, Théorie quantique des Intégrales de chemin Path integrals Quantum field theory Feldtheorie (DE-588)4016698-3 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Champs, Théorie quantique des Intégrales de chemin Path integrals Quantum field theory Feldtheorie Quantenfeldtheorie Pfadintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014957484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000819327 |
| work_keys_str_mv | AT dasashok fieldtheoryapathintegralapproach |